A baseball pitcher can throw a base ball at 150 ft/s. Can this pitcher hit the 200-ft ceiling of its game dome, if he was capable of giving a baseball an upward velocity of 85 ft/s, from a height of 7 ft? (Assume the ball is traveling as a free-falling body, and g = 32 ft/s2.)

Question

A baseball pitcher can throw a base ball at 150 ft/s. Can this pitcher hit the 200-ft ceiling of its game dome, if he was capable of giving a baseball an upward velocity of 85 ft/s, from a height of 7 ft? (Assume the ball is traveling as a free-falling body, and g = 32 ft/s2.)

Derive the motion equations, using an integration, NOTE: Even though g is given as a positive value, be sure to use the correct sign working this problem.

Give acceleration, "a", and the differentials dv and ds, using the value for g, the symbols v and dt, as needed, in each expression or differential.

Answer 1

surely by now you have derived the desired equation of motion.

h(t) = 7 + 85t - 16t^2
you know the max height is achieved at t = 85/32.

So, is h at least 200 at that time?

And why mention a speed of 150 ft/s if the upward velocity is only 85 ft/s? Do we need to assume an angle of release, and that the pitcher is standing some distance away from directly under the peak of the dome?