A frog jumps from a water lily leaf at an angle of 60degreesabove the horizontal (water surface). The maximum heightreached bythe frog during the leap is 1 m. Find the initial speedof the frog(when the frog leaves the water lily). Hint: use theprinciples ofconservation of energy. Ignore air resistance.

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30 Mar 2019

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A young bicyclist wants to jump over a stream. She is goingtouse a small ramp. If her speed at the top of the ramp is 5m/s

A) Howlong does it take for her to reach the maximum height?

B) Whatâs the maximum height (above the ground)?

C) Howlong does it take for the bike to hit the ground (orstream)?

D) Findthe velocity of the bike when it hits the ground (stream).

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A small package is fired off Earth's surface with a
speed v at a 45 degree angle with the local horizontal. It
reaches a maximum height h above the surface at h =
6370 km, a value equal to Earth's radius itself. What is
its speed when it reaches this height? Ignore any effects thatmight come from Earth's rotation or from air resistance.
(Hint: You will need to use two conservation equations and solvetwo equations in two unknowns.)

ANSWER IS 3.0 km/s

Walking by a pond, you find a rope attached to a tree limb 5.2 moff the ground. You decide to use the rope to swing out over thepond. The rope is a bit frayed but supports your weight. Youestimate that the rope might break if the tension is 82 N greaterthan your weight. You grab the rope at a point 4.6 m from the limband move back to swing out over the pond. Assume your weight to be650 N (about 145 lb).
(a) What is the maximum safe initial angle between the rope and thevertical so that it will not break during the swing?
Â°

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m/s

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