Question

24) A foot ball player can kick a football from ground level with an initial velocity
80ft/second
. Find the maximum horizontal distance the football travels and at
what angle? (Take g = 32)
​

Answer 1

Answer:

200 ft

45°

Step-by-step explanation:

Let say at angle α  ball is hit  with 80 ft/s

Horizontal Velocity = 80 Cosα  ft/s

Vertical Velocity = 80 Sinα  ft/s

Velocity at Peak = 0

Time to reach Peak  using V = u + at

a = -g = -32

=> 0 = 80Sinα - 32t

=> t =  80Sinα/32

=> t = 2.5 Sinα

Time to reah at peak = time to reach ground

=> total Time = 2 * 2.5Sinα = 5Sinα

Horizontal Distance = 80 Cosα * 5 Sinα

= 400 Cosα *Sinα

= 200 * 2*Cosα *Sinα

= 200 Sin2α

Maximum value of Sin2α = 1

Maximum horizontal distance = 200 * 1 = 200 ft

=> 2α = 90°

=> α = 45°