Question

A baseball is thrown from the stands 32 ft above the field at an angle of 30° up from the horizontal. When and how far away will the ball strike the ground if its initial speed is 32 ft/sec?

Use Ideal Projectile Motion equations:
x = xo + (vu cosα)t, = y=yo+(v0l sinα)t-1/2gt².
Note also that g≈ 32 ft/s² s2 in this unit system.

Answer 1

To calculate when and how far the baseball will hit the ground, use the projectile motion equations to find the time of flight with the vertical motion equation and then the horizontal distance with the horizontal motion equation, given the angle and speed at which the ball is thrown.

Step-by-step explanation:

To determine when and how far away a thrown baseball will hit the ground, we can use the provided projectile motion equations. Given the initial conditions of being thrown at an angle of 30° with a speed of 32 ft/s from a height of 32 ft, we will use the vertical motion equation to find the time it takes for the baseball to hit the ground, and then use the horizontal motion equation to find the horizontal distance covered.

For the vertical motion, the starting height, y0, is 32 ft, and the acceleration due to gravity, g, is 32 ft/s². The initial vertical speed is v0 sin(α), where α is 30°. The time t when the ball hits the ground can be calculated by setting the vertical motion equation to zero (when it hits the ground, y=0) and solving for t. After finding t, we use the horizontal motion equation to determine the horizontal distance, x, by multiplying the horizontal component of the initial velocity, v0 cos(α) (where α is 30°), by the time t.