Projectile Motion

Aaron GonzalezP3

ProjectileMotion

Scenario

The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 3 feet above the ground. It leaves the bat at an angle of θ degrees with the horizontal at a speed of 100 miles per hour.

Questions/Answers

Part A

Part C

Part D

Part B

Part D -

Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run.

Consider a projectile launched at a height h feet above the ground and at an angle θ with the horizontal. If the Velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = (v0 cos θ)t and y = -16t 2+ (v0 sin θ)t + h.

Part A -

Step 1 ) Convert the initial velocity into feet per second

Write a set of parametric equations for the path of the ball.

Step 2 ) Subsitute the initial velocity and height into the provided parametric equations

Part B -

Use a graphing utility to graph the path of the ball when θ = 15°. Is the hit a home run?

The hit is not a home run because the ball's x-position fell short of 400 feet.

Part C -

Use a graphing utility to graph the path of the ball when θ = 23°. Is the hit a home run?

This hit is a home run because the ball was still more than 10 feet in the air while its x-position crossed 400 feet.