A small rocket is fired directly upwards with an initial velocity of 100m/s, How many seconds will it take
to reach its maximum height?
Use the kinematic equation V = V0 + at defining up as positive.
Thus, t = (V-V0)/a
V0 is given as 100 m/s
At the top of the path V = 0
a = -9.81 m/s^2 (gravity)
Thus, t is about 10 seconds
t=(v-vo)/a
v=100m/sx10
a=9.81m/sx2
To find the time it takes for the rocket to reach its maximum height, we need to consider the motion of the rocket.
The initial velocity of the rocket is 100 m/s, and it is fired directly upwards. Assuming there is no air resistance, the rocket will experience only gravitational force pulling it downwards.
At the maximum height, the velocity of the rocket will become zero because it momentarily stops before it starts falling back down. Therefore, we can use the following equation to find the time it takes for the rocket to reach its maximum height:
v = u + at
Where:
v = final velocity (0 m/s at maximum height)
u = initial velocity (100 m/s)
a = acceleration due to gravity (-9.8 m/s^2, negative because it's in the opposite direction of the motion)
t = time
Rearranging the equation, we have:
0 = 100 - 9.8t
Solving for t:
9.8t = 100
t = 100 / 9.8
t ≈ 10.2 seconds
Therefore, it will take approximately 10.2 seconds for the rocket to reach its maximum height.