Use the following equation of motion from physics for an object moving in a vertical line and subject only to the force of gravity. where the positive direction is upward:
where s feet is the height of the object at t seconds , s_o feet is the initial height of the object, and v_0 feet/sec is the object's initial velocity.
21.) A rocket is fired vertically upward from the ground with an initial velocity of 560ft/sec. a.) Use (10) to write the equation of motion of the rocket and simulate the motion b.) Estimate how high the rocket will go and how long it takes the rocket to reach its highest point. c.) Confirm your estimates in part b Analytically. d.) Find the instantaneous velocity of the rocket at 10 sec and 25 sec. e.) Find the speed of the rocket at 10 sec & 25 sec. f.) Find the speed of the rocket when it reaches the ground.
a) v0 = 560 ft/s. (This is positive since the equation you were given assumed that the acceleration, which is downward, is negative.) Define the ground as s0 = 0 ft. (It can actually be defined to be any number you want, but this is standard.) Thus
Originally Posted by ^_^Engineer_Adam^_^
s = -16t^2 + 560t
b) By estimate I assume they mean graph it and guess where the highest point is. So graph it.
c) Analytically we know that v = 0 ft/s at maximum height. If you don't have Calculus at your disposal you probably know that v = v0 + at, so v = 560 - 32t. Set v = 0 ft/s and solve for t.
If you do know Calculus then v = ds/dt = 560 - 32t again. Either way t = 17.5 s.
d) v = 560 - 32t. Just plug in the times. I get v = 240 ft/s and v = -240 ft/s respectively.
e) The speed of the rocket is different from the velocity in one respect: speed does not have direction. The speed is the magnitude of the velocity so the answer is |v| = 240 ft/s in both cases.
f) When is the rocket on the ground? When s = 0 ft. Thus you need to solve the equation 0 = -16t^2 + 560t This will give you your t value, then use v = 560 - 32t. Alternately we have the equation
v^2 = v0^2 + 2a(s - s0)
We know that s = s0 = 0 ft here, so this means
v^2 = v0^2
v = (+/-)v0
Since all we care about is the speed, which is the magnitude of the velocity we have that:
|v| = |v0| = 560 ft/s, which had better be what you get using the first method as well.