A home run is hit in such a way that the baseball just clears a wall 11 m high, located 119 m from home plate. The ball is hit at an angle of 36° to the horizontal, and air resistance is negligible. (Assume that the ball is hit at a height of 1.0 m above the ground.) Find (a) the initial speed of the ball (b) the time it takes to reach the wall and (c) the velocity components and the speed of the ball when it reaches the wall. (assume the ball was hit at a height of 1 m above the ground.

Question

Syllable

Physics

1 November, 01:25

A home run is hit in such a way that the baseball just clears a wall 11 m high, located 119 m from home plate. The ball is hit at an angle of 36° to the horizontal, and air resistance is negligible. (Assume that the ball is hit at a height of 1.0 m above the ground.) Find (a) the initial speed of the ball (b) the time it takes to reach the wall and (c) the velocity components and the speed of the ball when it reaches the wall. (assume the ball was hit at a height of 1 m above the ground.

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Elvis · Answer 1

a) Equation of motion of a projectile motion is as follows

y = x tan∅ - 1/2 g x²/u²cos²∅

here y = 11-1 = 10 m, x = = 119 m, ∅ = 36

10 = 119 tan 36 - 4.9 119²/u² cos²36

u = 37.14 m/s

b) x component of u = u cos 36 = 30 m / s

time to reach wall = 119 / 30 = 3.97 s

c) x component of velocity will be the same.

y component will be as follows

u sin36 - g x 3.97 (v = u sin 36 - gt)

= - 17.07 m / s

ie it will be going in downward direction

resultant velocity = (30² + 17²) ¹/² = 34.48 m / s