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
The loudness of sound is the wave's ____.
Anni [7]
194db is the loudest Sound wave
5 0
3 years ago
Read 2 more answers
What is an organism's specific role in an ecosystem
Harman [31]
<span>Niche - </span><span>An organism's particular role in an ecosystem, or how it makes its living.</span>
7 0
3 years ago
Read 2 more answers
Which is true about atoms?
tiny-mole [99]

Answer:

A

Explanation:

6 0
2 years ago
Read 2 more answers
Do you think the plan for the skyscraper in California is appropriate based on its location? Why or why not? Your answer should
Anettt [7]

Answer:

No

Explanation:

No because like my other answer if we put to many diesels on it it will crack and little by little it will break eventually everyone will come tumbling into the water making them drown because they can't get the buckles loose or they wanted to save their families lives

5 0
3 years ago
A real battery with internal resistance 0.460 Ω and emf 9.00 V is used to charge a 56.0-µF capacitor. A 21.0-Ω resistor is put i
Margaret [11]

Answer: 1.176×10^-3 s

Explanation: The time constant formulae for an RC circuit is given below as

t =RC

Where t = time constant , R = magnitude of resistance = 21 ohms , C = capacitance of capacitor = 56 uf = 56×10^-6 F

t = 56×10^-6 × 21

t = 1176×10^-6

t = 1.176×10^-3 s

4 0
3 years ago
Read 2 more answers
Other questions:
  • In a young's double-slit experiment, the angle that locates the second dark fringe on either side of the central bright fringe i
    6·1 answer
  • Literary Analysis: Sound Devices. The words jump and stunt are examples of which sound device?
    7·1 answer
  • A material is said to be ductile if it
    13·1 answer
  • Why does pumping a soccer ball with an air pump increase the pressure inside the ball? the pump puts more gas particles inside t
    13·2 answers
  • A string of length L= 1.2 m and mass m = 20g is under 400 N of tension, its two ends are fixed. a. How many nodes will you see i
    6·1 answer
  • I have been trying to do number 2 and I just don’t know what the answer is if you can help me thank you so mush
    11·1 answer
  • What velocity is needed for a 2400 kg car to have the same amount of momentum as an 800 kg car?
    7·1 answer
  • Someone please help me!!
    5·1 answer
  • Which two statements about redox reactions are true? HELP ASAP!!!!
    6·1 answer
  • The weight of an astronaut on the moon is the same as on Earth.<br> True<br> False
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!