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.

You are watching: Find the angle θ above the horizontal at which the projectile should be fired.

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.

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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.

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? = | ? ? |

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