Throwing a football

At a given instant the football player at A throws a football C with a velocity of 20 m / s in the direction shown. Player B is 15 m away from A when A starts to throw the football.

Part A
Determine the constant speed at which the player at B must run so that he can catch the football at the same elevation at which it was thrown. Express your answer to three significant figures and include the appropriate units.

Determine the time the ball takes to finish its trajectory

y: V = V₀ +a*t

When V = 0 when the ball is at half its trajectory

So, -V₀ = a*t

V₀ = 20*sin(60) = 17.3 m/s

-17.3 = -9.8*t

t = 1.767 s at half the trajectory

2t = 3.53 s at the full trajectory

Now determine the distance the ball traveled from A

Distance s = V * t because there is no acceleration or deceleration in the x axis and V_x = 20cos(60) = 10 m/s

s = 10 * 3.53 = 35.3 m

So if the ball falls 3.53 seconds after is thrown at 35.3 m from A and B is already 15 m from A then he has to run 20.3 m to catch it in 3.53 seconds. So,

V = 20.3 m / 3.53 s = 5.75 m /s

Calculate the magnitude of the relative velocity of the football with respect to B at the instant the catch is made. Express your answer to three significant figures and include the appropriate units.

When the ball is caught the Velocity is the same as when it was thrown but going downwards, so

V_X when it was thrown = V_X when it was caught

V_Y when it was thrown = - V_Y when it was caught

Relative X speed = Speed of ball - Speed of player = 10 - 5.75 = 4.25 m/s

Relative Y speed = Speed of ball - Speed of player = -17.3 - 0 = -17.3 m/s

Pythagorean theorem will get you the answer now,

Relative speed = 17.8 m/s

Determine the angle θv of vC/B (counterclockwise from the positive x axis). Express your answer to three significant figures and include the appropriate units.

The angle can be determined by doing the inverse tangent:

tan^-1 (Relative Y/Relative X) = -76.2 degrees remember is negative from the positive x axis.

Calculate the magnitude of the relative acceleration of the football with respect to B at the instant the catch is made. Express your answer to three significant figures and include the appropriate units.

The magnitude is super simple, The player is not accelerating at the x axis, and is not even moving in the y axis so is not accelerating up and down either. The ball is not accelerating in the x axis and is only accelerating in the Y axis, so you only use the Y acceleration difference:

Y relative acceleration = g - 0 = 9.8 m/s²