My A football receiver running straight downfield at 5.30 m/s is 12.0 m in front

Question

My A football receiver running straight downfield at 5.30 m/s is 12.0 m in front of the quarterback when a pass is thrown downfield at 310 above the horizon (see the figure below). 5.30 m/s 5.30 m/s 4 -12.0 m- Ir the receiver never changes speed and the ball is caught at the same helight from which it was thrown, find the footbal's initial speed, the amount of time the football spend in the air, and the distance between the quarterback and the receiver when the catch is made (a) the football's initial speed (in m/s) m/s (b) the amount of time the football spends in the air (in s) () the distance between the quarterback and the receiver when the catch is made (in m

Explanation / Answer

time of flight

T = 2*vo*sintheta/g

along horizontal

distance travelled by receiver = 5.3*T

for foot ball

range R = vo^2*sin(2theta)/g

vo^2*sin(2theta)/g = 12 + 5.3*T

vo^2*sin(2theta)/g = 12 + 5.3*2*vo*sintheta/g

v0^2*sin(62)/9.8 = 12 + (5.3*2*v0*sin31/9.8)

v0 = 15.03 m/s <<<-----ANSWER

================

T = 2*v0*sintheta/g

T = 2*15.03*sin31/9.8

T = 1.58 s <<<<----------ANSWER

===========================================

(c)

R = v0^2*sin(2theta)/g

R = 15.03^2*sin62/9.8

R = 20.35 m <<<<----------ANSWER

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