A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 7.10 seconds later.
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To find the height at which the bolt fell off the rocket, we can use the equations of motion.
1. First, we need to calculate the time it took for the bolt to reach the ground after falling off the rocket. We are given that it took 7.10 seconds for the bolt to hit the ground after it fell off.
2. Since the bolt was falling freely under gravity, the time it took to reach the ground can be found using the equation for the vertical motion:
`h = (1/2) * g * t^2`
where h is the height (unknown), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time (7.10 seconds).
Rearranging the equation, we have:
`h = (1/2) * 9.8 * (7.10)^2`
Calculate the value of h to find the height at which the bolt fell off the rocket.
3. Now, to find the height at which the bolt fell off the rocket, we need to calculate the distance covered by the rocket during the first 4 seconds after liftoff.
The equation for the distance covered during constant acceleration is:
`d = v_0 * t + (1/2) * a * t^2`
where d is the distance (unknown), v_0 is the initial velocity of the rocket (which we assume is 0 since it just started to accelerate), a is the constant acceleration (which we're given), and t is the time interval (4 seconds).
Rearranging the equation, we have:
`d = (1/2) * a * t^2`
Plug in the value of t (4 seconds) and the given value of a to calculate the distance d covered by the rocket.
4. To find the height at which the bolt fell off the rocket, we subtract the distance covered by the rocket from the height at which the bolt hit the ground.
`Height of falling off = Height at which bolt hit the ground - Distance covered by rocket`
Substitute the values obtained in the previous steps to find the height at which the bolt fell off the rocket.