On planet X, you drop a 25.0 kg stone from rest and measure its speed at various
ID: 2005200 • Letter: O
Question
On planet X, you drop a 25.0 kg stone from rest and measure its speed at various times. Then you use the data you obtained to construct a graph of its speed v as a function of time t. (The graph shows a velocity of 15m/s at time 1s and 30 m/s at time 2s)a) What is g on Planet X
b) An astronaut drops a piece of equipment from rest out of the landing module, 8.5 m above the surface of Planet X. How long will it take this equipment to reach the ground?
c) How fast will this equipment be moving when it reaches the ground?
d) How fast would an astronaut have to project an object straight upward to reach a height of 25.4 m ?
How long would it take the object to reach a height of 15 m? For an object thrown upward there are two times it would be at any height. Give the going up answer and the going down answer.
Explanation / Answer
From thye data:
The speed of the object at t= 0 is u = 0 (dropped from rest)
The speed at t = 1 s is v1 = 15 m/s
The speed at t = 2 s is v2 = 30 m/s
a)
The eqution of motion of the object at the end of 2 s is
v2 = u + gt
Where g is the acceleration due to gravity on the planet
30 m/s = 0 + (g)(2 s)
g = 15 m/s2
b)
The time taken by the object to reach the ground from a height h = 8.5 m is
h = 0.5gt2
8.5 m = 0.5(15 m/s2)t2
t = 1.065 s
c)
The speed of the object at the time of reaching the ground is
v2 = 2gh
v2 = 2(15 m/s2)(8.5 m)
v = 15.97 m/s
d)
The height to be reached is h = 25.4 m
The initial speed required will be
v2- u2 = 2g(-h)
-u2 = -2gh
u2 = 2gh
u = 27.6 m/s
e)
The time taken by the object to reach height of 15 m is
v = u - gt
0 = u - gt
u = gt
t = 1.84 s (moving upwards)
The time taken by the object to fall back to ground
h = 0.5gt2
15 m = 0.5(15 m/s2)t2
t = 1.41 s (moving downwards)
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