Question

A baseball player leads off the game and hits a long home run. the ball leaves the bat at a height of 4ft above the ground and an angle of 32 degrees from the horizontal with a velocity of 131 ft/s.

write a set of equations that model the scenario.

Answer 1

time = 4.4 s

horizontal distance = 488.8 m

Explanation:

Height, h = 4 ft

Angle, A = 32 degree above X axis

velocity, u = 131 ft/s

Let the time taken is t.

Use second equation of motion

`h = u t + 0.5 gt^2\\\\- 4 = 131 sin 32 t - 16 t^2\\\\16t^2 - 69.4t - 4 = 0\\\\t=(69.4\pm √(4816.36 +256))/(32)\\\\t = (69.4\pm71.2)/(32)\\\\t = - 0.05625 s, 4.4 s`

So, time is 4.4 s.

The horizontal distance is

d = u cos A t

d = 131 cos 32 x 4.4 = 488.8 m