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
GaryK [48]
2 years ago
15

A quarterback is set up to throw the football to a receiver who is running with a constant velocity v⃗ rv→rv_r_vec directly away

from the quarterback and is now a distance DDD away from the quarterback. The quarterback figures that the ball must be thrown at an angle θθtheta to the horizontal and he estimates that the receiver must catch the ball a time interval tctct_c after it is thrown to avoid having opposition players prevent the receiver from making the catch. In the following you may assume that the ball is thrown and caught at the same height above the level playing field. Assume that the y coordinate of the ball at the instant it is thrown or caught is y=0y=0 and that the horizontal position of the quarterback is x=0x=0.
Physics
1 answer:
Artist 52 [7]2 years ago
6 0

Answer:

a) V_o,y = 0.5*g*t_c

b) V_o,x = D/t_c - v_r

c) V_o = sqrt ( (D/t_c - v_r)^2 + (0.5*g*t_c)^2)

d)  Q = arctan ( g*t_c^2 / 2*(D - v_r*t_c) )

Explanation:

Given:

- The velocity of quarterback before the throw = v_r

- The initial distance of receiver = r

- The final distance of receiver = D

- The time taken to catch the throw = t_c

- x(0) = y(0) = 0

Find:

a) Find V_o,y, the vertical component of the velocity of the ball when the quarterback releases it.  Express V_o,y in terms of t_c and g.

b) Find V_o,x, the initial horizontal component of velocity of the ball.   Express your answer for V_o,x in terms of D, t_c, and v_r.

c) Find the speed V_o with which the quarterback must throw the ball.  

   Answer in terms of D, t_c, v_r, and g.

d) Assuming that the quarterback throws the ball with speed V_o, find the angle Q above the horizontal at which he should throw it.

Solution:

- The vertical component of velocity V_o,y can be calculated using second kinematics equation of motion:

                               y = y(0) + V_o,y*t_c - 0.5*g*t_c^2

                              0 = 0 + V_o,y*t_c - 0.5*g*t_c^2

                               V_o,y = 0.5*g*t_c

- The horizontal component of velocity V_o,x witch which velocity is thrown can be calculated using second kinematics equation of motion:

- We know that V_i, x = V_o,x + v_r. Hence,

                               x = x(0) + V_i,x*t_c

                               D = 0 + V_i,x*t_c

                               V_o,x + v_r = D/t_c

                                V_o,x = D/t_c - v_r

- The speed with which the ball was thrown can be evaluated by finding the resultant of V_o,x and V_o,y components of velocity as follows:

                           V_o = sqrt ( V_o,x^2 + V_o,y^2)

                          V_o = sqrt ( (D/t_c - v_r)^2 + (0.5*g*t_c)^2)

       

- The angle with which it should be thrown can be evaluated by trigonometric relation:

                            tan(Q) = ( V_o,y / V_o,x )

                            tan(Q) = ( (0.5*g*t_c)/ (D/t_c - v_r) )

                                   Q = arctan ( g*t_c^2 / 2*(D - v_r*t_c) )

                           

                               

You might be interested in
Define what is energy and work​
Mashutka [201]

The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force.

8 0
2 years ago
During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 33.5 rad/s. Find the angular displ
zavuch27 [327]

Answer: angular displacement in rad = 3038.45 rad

angular displacement in rev = 483.589 rev

Explanation: mathematically

Angular velocity = angular displacement / time taken.

Angular velocity = 33.5 rad/s, time taken = 90.7s

33.5 = angular displacement /90.7

Angular displacement = 33.5 * 90.7 = 3038.45 rad

But 1 rev =2π

Hence 3038.45 rad to rev is

3038.45/2π = 483.599 rev

7 0
3 years ago
Read 2 more answers
A cheetah can accelerate from rest at the rate of 4m /s
lesya [120]
Acceleration of cheetah (a) = 4m/s²
time = 10s
initial velocity(u) = 0
final velocity = v
distance travelled = s

v = u +at = 0 + 10×4 = 40m/s
s = (v²-u²)/2a = 40²/(2×4) = 1600/8 = 200m
   
6 0
3 years ago
A certain lightning bolt moves 50.0 C of charge. How many units of fundamental charge is this?
liubo4ka [24]
Answer: There are number of electrons.
Explanation:
We are given 50 Coulombs of charge and we need to find the number of electrons that can hold this much amount of charge. So, to calculate that we will use the equation:

where,
n = number of electrons
Charge of one electron =
Q = Total charge = 50 C.
Putting values in above equation, we get:

Hence, there are number of electrons.
7 0
3 years ago
I don’t understand how to do this
anzhelika [568]

Explanation:

A) Use Hooke's law to find the spring constant.

F = kx

40 N = k (0.4 m)

k = 100 N/m

B) Period of a spring-mass system is:

T = 2π √(m / k)

T = 2π √(2.6 kg / 100 N/m)

T = 1 s

Frequency is the inverse of period.

f = 1 / T

f = 1 Hz

5 0
2 years ago
Other questions:
  • HELP!!
    11·2 answers
  • A swan on a lake gets airborne by flapping its wings and running on top of the water. If the swan must reach a velocity of 6.40
    13·1 answer
  • How do electromagnetism and gravitation differ from the strong and weak nuclear forces?
    11·1 answer
  • How do you find the g field at a point between 2 masses?
    12·1 answer
  • The engine on a fighter airplane can exert a force
    9·1 answer
  • Student bikes to school by traveling first dN = 1.10 miles north, then dW = 0.300 miles west, and finally dS = 0.200 miles south
    15·1 answer
  • a sound wave has a frequency of 1192 hertz. all sound waves in air travel at 322m/s. find the wave length of the sound wave
    12·1 answer
  • A ball rolls up a ramp with a velocity of 8.0 m/s. How high up the ramp does it travel?
    8·1 answer
  • What do the plastic jars of the air capacitor represent in an electrical capacitor? The parallel conducting plates The source of
    14·1 answer
  • Is a neutron positive ornegative
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!