1. A projectile is fired with speed v0 at an angle ? from thehorizontal as shown in the figure

Part A

Find the highest point in the trajectory, H.

Express the highest point in terms of the magnitude of theacceleration due to gravity g, the initial velocity v0, and theangle ?.

H =

Part B

What is the range of the projectile, R?

Express the range in terms of v0, ?, and g.

R =

?

Consider your advice to an artillery officer who has thefollowing problem. From his current postition, he must shoot over ahill of height H at a target on the other side, which has the sameelevation as his gun. He knows from his accurate map both thebearing and the distance R to the target and also that the hill ishalfway to the target. To shoot as accurately as possible, he wantsthe projectile to just barely pass above the hill.

Part C

Find the angle ? above the horizontal at which the projectileshould be fired.

Express your answer in terms of H and R.

? =

?

Part D

What is the initial speed?

Express v0 in terms of g, R, and H.

v0 =

?

Part E

Find tg, the flight time of the projectile.

Express the flight time in terms of H and g.

tg =

?

2. A softball is hit over a third baseman's head with somespeed

v0 at an angle ? above the horizontal. Immediately after theball is hit, the third baseman turns around and begins to run at aconstant velocity V=7.00m/s. He catches the ballt=2.00s later atthe same height at which it left the bat. The third baseman wasoriginally standing L=18.0m from the location at which the ball washit.

Part A

Find v0. Use g=9.81m/s2 for the magnitude of the accelerationdue to gravity.

Express the initial speed numerically in units of meters persecond to three significant figures.

v0 =

? m/s

Part B

Find the angle ? in degrees.

Express your answer numerically in degrees to three significantfigures.

? =

? ?

H R X