A rocket blasts off. In 10.0 seconds it is at 10,000 ft, traveling at 3600 mph. Assuming the direction is up, calculate the acceleration.
To calculate the acceleration, we need to use the formula:
Acceleration (a) = change in velocity (Δv) / change in time (Δt)
First, we need to convert the given velocity from mph to ft/s, as the units need to be consistent. Since 1 mile = 5280 feet and 1 hour = 3600 seconds, we multiply the velocity by these conversion factors:
Velocity in ft/s = 3600 mph * (5280 ft/1 mile) * (1 hour/3600 seconds) = 5280 ft/s
The velocity is given at the starting point (10 seconds), but we need the velocity at the ending point (10,000 ft).
To find that, we can use the formula:
Final velocity (v) = Initial velocity (u) + (acceleration * time)
Since the rocket is starting from rest, the initial velocity (u) is 0. Hence the formula becomes:
Final velocity (v) = 0 + (acceleration * time)
Rearranging the formula, we get:
Acceleration (a) = (Final velocity - Initial velocity) / time
Now, we can substitute the values into the formula:
Acceleration (a) = (5280 ft/s - 0 ft/s) / 10.0 seconds
Acceleration (a) = 5280 ft/s / 10.0 seconds
Acceleration (a) = 528 ft/s²
Therefore, the acceleration of the rocket is 528 ft/s².