An object that is launched straight up from the ground reachesmaximum height H and falls straight back down to the ground,hitting it T seconds after launch. Neglect any effects due to airresistance.

(a) Express the average speed over the entire trip as a function ofH and T.
vav =
(b) Express the average speed for the same interval of time as afunction of the initial launch speed v0.
vav =

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An object that is launched straight up from the ground, reaches amaximum height H, and falls straight back down to the ground,hitting it T seconds after launch. Neglect any effects due to airresistance. (a) Express the average speed for the entire trip as afunction of H and T. (b) Express the average speed for the sameinterval of time as a function of the initial launch speedv0.

A wheeled cart sits stationary on a track. The cart has a
funnel mounted on its top, and a steel ball sits in thefunnel,
as shown. Inside the funnel is a spring launcher which fires
the ball straight up. Thus when launched, the ball goes up and thenfalls back
into the funnel.
The time from the launch until the balls fall back into the funnelis t. The vertical speed
of the launched ball when it leaves the funnel is v0.
The mass of the cart, including the funnel and spring launcher, isM. The mass of the steel
ball is m. Assume that air resistance and friction are negligible.Assume that the mass of the wheels
of the cart is negligible compared to M. Assume that the track isalways long enough for
the cart to be on it between when the ball is launched and when itreturns.
PART A:
What is t, the time from the ball being launched until it fallsback into the funnel?
PART B:
Now the cart is moving to the right
with constant speed V. The ball is
launched and the cart continues
moving with speed V. When the ball returns to the same initialheight above the track, does it land in the funnel, to the rightof
the funnel, or to the left of the funnel?
PART C:
If your answer to B was that the ball lands in the funnel, showthat your answer is correct.
For any other answer, what is the distance from the center of thefunnel to the center of
the ball when the ball returns to the same initial height above thetrack?
PART D:
A constant force F is exerted on the
cart. When the cartâs speed is V, the ball
is launched. When the ball returns to the
same initial height above the track, does
it land in the funnel, to the right of the
funnel, or to the left of the funnel?
PART E:
If your answer to D was that the ball lands in the funnel, showthat your answer is correct.
For any other answer, what is the distance from the center of thefunnel to the center of
the ball when the ball returns to the same initial height above thetrack?
PART F:
The cart is rolling down an inclined plane
which is at an angle ? to the horizontal.
When the cartâs speed is V, the ball is
launched. When the ball returns to the same
initial perpendicular distance above the
track, does it land in the funnel, to the right
of the funnel, or to the left of the funnel?
PART G:
If your answer to F was that the ball lands in the funnel, showthat your answer is correct.
For any other answer, what is the distance from the center of thefunnel to the center of
the ball when the ball returns to the same initial perpendiculardistance above the track?

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