Two identical grasshoper jumps into the air with the same initial speed and expe
ID: 1416986 • Letter: T
Question
Two identical grasshoper jumps into the air with the same initial speed and experience no air resistance. Grasshoper A goes straight up, but grasshoper B goes up at a 66 degrees angle above the hoirzontal. Which of the following statments about these grasshopers are correct? (There could be more than one correct choice).
A) at their highest point, both of them have the same amount of kinetic energy.
B) at their highest point, grasshoper A has more gravitational potential energy than grasshoper B.
C) at their highest point , both of them have the same amount of gravitational potential energy.
D) at their highest point ,both of them have the same amount of mechanical energy.
E) at their highest point, grasshoper B is moving faster than grasshoper A.
Explanation / Answer
A) at their highest point, both of them have the same amount of kinetic energy.
FALSE: By logic of ANS B they both start with the same TE, but one has a greater GPE at max height, which means that one has a smaller KE.
B) at their highest point, grasshoper A has more gravitational potential energy than grasshoper B.
TRUE: GPE = mgH > mgh = gpe for B because max height for A is H > h.
C) at their highest point , both of them have the same amount of gravitational potential energy.
FALSE: the straight up will reach a higher max height and thus greater GPE.
D) at their highest point ,both of them have the same amount of mechanical energy.
TRUE: I dislike the term "mechanical energy," but they both started with the same total energy TE = KE = 1/2 mU^2 where U is their jumping speed.
E) at their highest point, grasshoper B is moving faster than grasshoper A.
TRUE: A isn't moving at all at max height, but B has a bit of XX direction speed Ux = U cos(66)
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