Matt and his friends are enjoying an afternoon at a baseball game. A batter hits a towering homerun, and
Matt shouts, âWow, that must have been 110 feet high!â The ball was 4 feet off the ground when the batter
hit it, and the ball came off the bat traveling vertically at 80 feet per second.
a. Model the ballâs height h (in feet) at time t (in seconds) using the projectile motion model h(t) = 16t2 + v0t + h0 where v0 is the projectileâs initial vertical velocity (in feet per second) and h0 is the projectileâs initial height (in feet). Use the model to write an equation based on Mattâs claim, and then determine whether Mattâs claim is correct.
b. Did the ball reach a height of 100 feet? Explain.
c. Let hmax be the ballâs maximum height. By setting the projectile motion model equal to hmax, show
how you can find hmax using the discriminant of the quadratic formula.
d. Find the time at which the ball reached its maximum height.
Matt and his friends are enjoying an afternoon at a baseball game. A batter hits a towering homerun, and
Matt shouts, âWow, that must have been 110 feet high!â The ball was 4 feet off the ground when the batter
hit it, and the ball came off the bat traveling vertically at 80 feet per second.
a. Model the ballâs height h (in feet) at time t (in seconds) using the projectile motion model h(t) = 16t2 + v0t + h0 where v0 is the projectileâs initial vertical velocity (in feet per second) and h0 is the projectileâs initial height (in feet). Use the model to write an equation based on Mattâs claim, and then determine whether Mattâs claim is correct.
b. Did the ball reach a height of 100 feet? Explain.
c. Let hmax be the ballâs maximum height. By setting the projectile motion model equal to hmax, show
how you can find hmax using the discriminant of the quadratic formula.
d. Find the time at which the ball reached its maximum height.
