At a given instant the football player at A throws a football C with a velocity

Question

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.
(Figure 1)

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.

Part B

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.

Part C

Determine the angle v of vC/B (counterclockwise from the positive x axis).

Express your answer to three significant figures and include the appropriate units.

Part D

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.

Figure 1 of 1

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.
(Figure 1)

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.

vB =

Part B

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.

vC/B =

Part C

Determine the angle v of vC/B (counterclockwise from the positive x axis).

Express your answer to three significant figures and include the appropriate units.

v =

Part D

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.

aC/B =

Figure 1 of 1

20 m/s 60 15 m

Explanation / Answer

A)

time of flight = 2*u/g = (2*20*sin60)/9.8 = 3.535 sec

(20*cos60 - Vb)*3.535 = 15

Vb = 5.76 m/sec

B)

relative velocity with respect to B.

Vx = 10 - 5.76 = 4.24 m/s

Vy = -20*sin60 = -17.32 m/sec

V = sqrt(Vx^2 + Vy^2) = 17.83 m/s

C)

theta = tan inverse ( -17.32/4.24) = 283.75 degree

D) relative acceleration = g {9.8 m/s^2 downward}

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