There are a couple of problems that I need some guidance/help on.
Any helpful input is appreciated.
Here they are:
1) A dynamite blast blows a heavy rock straight up with a launch of 160 ft/sec. It reaches a height of s(t)=160t-16t^2 after t seconds.
a. Find the maximum height of the rock.
For this one I set the function equal to zero and solved for t. I got t=5 seconds. I plugged it into the original function and got 400ft. (not sure if I did it right)
b. How long is the rock in the air? (5x2 = 10seconds?)
c. When is the maximum height reached? (5 seconds?)
d. How fast is the rock going at 256 ft.? (no idea)
e. Find the average velocity between t=3 and t=8. (-16ft/sec ?)
2) A bomb is dropped from an airplane at an altitude of 14,400 ft.
s(t)=-16t^2+vto+so
a. Find the position function, s(t)
b. How long will it take to reach the ground?
c. The plane moves horizontally at 600 mph. How far will the bomb be from the plane (horizontal distance from the plane) when it hits the ground?
3) A projectile is fired upward from the earth's surface with an inital velocity of 256 ft./sec. Use the general position function: s(t)=-16t^2+vot+so. Find each of the following.
a. The specific position function
b. The specific velocity function
c. When does the projectile hit the ground?
d. The velocity when the projectile hits the ground?
e. The speed when the projectile hits the ground?
f. The average velocity between t=0 and t = 10 seconds.
g. The instantaneous velocity at t=0 and t=10 seconds.
h. When does the projectile reach its maximum height?
i. What is the maximum height?
j. What is the velocity at the instant the projectile reaches its maximum height?
k. What is the acceleration of the particle?
Thanks in advance.