Question

A baseball is thrown at a 28° angle and an initial velocity of 70 m/s. Assume no air resistance. How far did the ball travel horizontally when it hit the ground?
414.9 m
500.76 m
510.2 m
130.5 m

Answer 1

Answer:

414.9 m

Explanation:

First, become familiar with the horizontal, and vertical vector components.

Vertical vector: Vy = V × sin (θ).

Horizontal vector: Vx = V × cos(θ).

Distance traveled = Velocity vector × time in the air.

Time in the air given Vy = 2 × Vy / g (in respect to the metric of the vector).

Range of the projectile = Vx² / g

Time in the air given Vx = (Vx + √(Vx)² + 2gh) / g.

Given a 28° angle with an initial velocity of 70m/s, we have enough information to calculate!

Vx = 70 m/s × cos(28°) ≈ 61.806 m/s

Vy = 70 m/s × sin(28°) ≈ 32.863 m/s

t = 2 × Vy / g

t = 2 × ≈32.863 / 9.8

t = ≈65.726 / 9.8

t ≈ 6.7 s

Distance traveled (horizontal) = Vx × t = 61.806 × 6.7 ≈ 414.9 m