1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Westkost [7]
3 years ago
13

A quarterback passes a football from height h = 2.1 m above the field, with initial velocity v0 = 13.5 m/s at an angle θ = 32° a

bove horizontal. Assume the ball encounters no air resistance, and use a Cartesian coordinate system with the origin located at the ball's initial position.
(a) Create an expression for the football’s horizontal velocity, vfx, when caught by a receiver in terms of v0, θ, g, and h.

(b) The receiver catches the football at the same height as released by the quarterback. Create an expression for the time, t f, the football is in the air in terms of v0, θ, g, and h.

(c) The receiver catches the ball at the same vertical height above the ground it was released. Calculate the horizontal distance, d in meters, between the receiver and the quarterback.
Physics
1 answer:
alisha [4.7K]3 years ago
4 0

Answer:

a)    x = v₀² sin 2θ / g

b)    t_total = 2 v₀ sin θ / g

c)    x = 16.7 m

Explanation:

This is a projectile launching exercise, let's use trigonometry to find the components of the initial velocity

        sin θ = v_{oy} / vo

        cos θ = v₀ₓ / vo

         v_{oy} = v_{o} sin θ

         v₀ₓ = v₀ cos θ

         v_{oy} = 13.5 sin 32 = 7.15 m / s

         v₀ₓ = 13.5 cos 32 = 11.45 m / s

a) In the x axis there is no acceleration so the velocity is constant

         v₀ₓ = x / t

          x = v₀ₓ t

the time the ball is in the air is twice the time to reach the maximum height, where the vertical speed is zero

          v_{y} = v_{oy} - gt

          0 = v₀ sin θ - gt

          t = v_{o} sin θ / g

         

we substitute

       x = v₀ cos θ (2 v_{o} sin θ / g)

       x = v₀² /g      2 cos θ sin θ

       x = v₀² sin 2θ / g

at the point where the receiver receives the ball is at the same height, so this coincides with the range of the projectile launch,

b) The acceleration to which the ball is subjected is equal in the rise and fall, therefore it takes the same time for both parties, let's find the rise time

at the highest point the vertical speed is zero

          v_{y} = v_{oy} - gt

          v_{y} = 0

           t = v_{oy} / g

           t = v₀ sin θ / g

as the time to get on and off is the same the total time or flight time is

           t_total = 2 t

           t_total = 2 v₀ sin θ / g

c) we calculate

          x = 13.5 2 sin (2 32) / 9.8

          x = 16.7 m

You might be interested in
When conduction electrons pass through a device with resistance, which describes their energy?
Aleksandr-060686 [28]

Answer:

a) their potential energy increases.

Explanation:

Ohm's Law is

R= V/I

Where R= Resistance

V= potential difference or potential energy

I= current or conduction electron flow rate

Clearly R and V are directly proportional i-e Potential energy increases with resistance.

3 0
2 years ago
James threw a ball vertically upward with a velocity of 41.67ms-1 and after 2 second David threw a ball vertically upward with a
Reptile [31]

Answer:

When have passed 3.9[s], since James threw the ball.

Explanation:

First, we analyze the ball thrown by James and we will find the final height and velocity by the time two seconds have passed.

We'll use the kinematics equations to find these two unknowns.

y=y_{0} +v_{0} *t+\frac{1}{2} *g*t^{2} \\where:\\y= elevation [m]\\y_{0}=initial height [m]\\v_{0}= initial velocity [m/s] =41.67[m/s]\\t = time passed [s]\\g= gravity [m/s^2]=9.81[m/s^2]\\Now replacing:\\y=0+41.67 *(2)-\frac{1}{2} *(9.81)*(2)^{2} \\\\y=63.72[m]\\

Note: The sign for the gravity is minus because it is acting against the movement.

Now we can find the velocity after 2 seconds.

v_{f} =v_{o} +g*t\\replacing:\\v_{f} =41.67-(9.81)*(2)\\\\v_{f}=22.05[m/s]

Note: The sign for the gravity is minus because it is acting against the movement.

Now we can take these values calculated as initial values, taking into account that two seconds have already passed. In this way, we can find the time, through the equations of kinematics.

y=y_{o} +v_{o} *t-\frac{1}{2} *g*t^{2} \\y=63.72 +22.05 *t-\frac{1}{2} *(9.81)*t^{2} \\\\y=63.72 +22.05 *t-4.905*t^{2} \\

As we can see the equation is based on Time (t).

Now we can establish with the conditions of the ball launched by David a new equation for y (elevation) in function of t, then we match these equations and find time t

y=y_{o} +v_{o} *t+\frac{1}{2} *g*t^{2} \\where:\\v_{o} =55.56[m/s] = initial velocity\\y_{o} =0[m]\\now replacing\\63.72 +22.05 *t-(4.905)*t^{2} =0 +55.56 *t-(4.905)*t^{2} \\63.72 +22.05 *t =0 +55.56 *t\\63.72 = 33.51*t\\t=1.9[s]

Then the time when both balls are going to be the same height will be when 2 [s] plus 1.9 [s] have passed after David throws the ball.

Time = 2 + 1.9 = 3.9[s]

4 0
3 years ago
Air, considered an ideal gas, is contained in an insulated piston-cylinder assembly outfitted with a paddle wheel. It is initial
Maru [420]

Our data are,

State 1:

P_1= 10psi=68.95kPa\\V_1 = 1ft^3=0.02831m^3\\T_1 = 100\°F = 310.93K

State 2:

P_2 =5psi=34.474kPa\\V_2 = 3ft^3=0.0899m^3

We know as well that 3BTU=3.16kJ/K

To find the mass we apply the ideal gas formula, which is given by

P_1V_1=mRT_1

Re-arrange for m,

m= \frac{P_1V_1}{RT_1}\\m= \frac{68.95*0.02831}{(0.287)310.9}\\m=0.021893kg=0.04806lbm\\

Because of the pressure, temperature and volume ratio of state 1 and 2, we have to

\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}

Replacing,

T_2 = \frac{P_2V_2}{P_1V_1}T_1\\T_2 =\frac{34.474*0.0844}{68.95*0.02831}*310.93\\T_2 = 464.217K=375.5\°F

For conservative energy we have, (Cv = 0.718)

W = m C_v = 0.718  \Delta T +dw\\dw = W - mv\Delta T\\dw = 3.16-(0.0218*0.718)(454.127-310.93)\\dw = 0.765kJ=0.72BTU

3 0
3 years ago
In what direction would the particles in this wave move, relative to the direction of wave travel?
Setler79 [48]
Everywhere particles dont stay in one place they move elsewhere
7 0
2 years ago
Read 2 more answers
Please help me with these two questions
Andre45 [30]

Answer:

The kinetic energy would decrease because it has less mass

Explanation:

A battery

4 0
3 years ago
Other questions:
  • I am sitting on a train car traveling horizontally at a constant speed of 50 m/s. I throw a ball straight up into the air.
    15·1 answer
  • Jana is observing a young autistic boy in a preschool classroom. Her job is to note each time the boy gets up from his chair wit
    15·1 answer
  • a 2.0 kg block slides on the horizontal, frictionless surface until it counters a spring force constant with
    5·1 answer
  • In which place moutain or terai,the value of g is more and why?​
    10·1 answer
  • Are bases chemically the same as acids true or false
    15·1 answer
  • What happens when sodium Hydroxide reacts with Hydrochloric acid?​
    15·2 answers
  • If you increase the force on an item without changing the mass you increase acceleration? true or false?
    8·1 answer
  • 16 grams of ice at –32°C is to be changed to steam at 182°C. The entire process requires _____ cal. Round your answer to the nea
    7·1 answer
  • What is the most common kind of element in the solar wind?
    12·1 answer
  • A hiker is at the bottom of a canyon facing the canyon wall closest to her. She is 280.5 meters from the wall and the sound of h
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!