Question

a dynamite blast propels a heavy rock straight up with a launch velocity of 160ft/sec (about 109 mph). Write a position for the height of the rock.

a. How high does the rock go?
b. What is the velocity and speed of the rock when it is 256 ft above the ground on the way up? On the way down?
c. What is the acceleration of the rock at any time t during its flight (after the blast)?
d. When does the rock hit the ground?

Answer 1

Are you familiar w/ parabolic motion?

\[x = x_0 + v_0 t + \frac{1}{2}at^2\]

Answer 2

at maximum hseight velocity = 0
using v^2 = u^2 + 2as
0 = 160^2 - 2*32 * s

s = required distance

Answer 3

that is confusing me

Answer 4

Is this calculus physics or no?

Answer 5

that formula relates initial velocity u , and final velocity v, in this case a = acceleration due to gravity and s = distance traveled

it is one of the formula for motion with constant acceleration

Answer 6

it is calc ab

Answer 7

Well, then another option would be to differentiate the equation in the first response. The first derivative of motion is velocity. Where the velocity is 0, there is maximum height (in this case).

Answer 8

*first derivative of displacement.

Answer 9

yes - these equations are all derived using calculus

Answer 10

v_0 = 160 ft/sec

y(t) = vt - .5gt^2, g = -32.2 ft/s^2

v(t) = a*t

a. How high does the rock go?

Use the velocity equation to solve for t when v=0.

b. What is the velocity and speed of the rock when it is 256 ft above the ground on the way up? On the way down?

The velocity and speed have the same magnitude, but velocity includes direction.
Plug in 256 ft to the position equation to solve for t, then use velocity equation.

There is a third equation which is a combination of the position and velocity equations,
v^2 = 2ay, that is more direct. Try it both ways to see how they work.

c. What is the acceleration of the rock at any time t during its flight (after the blast)?

hint: It stays constant.

d. When does the rock hit the ground?

solve y(t) =0.

Answer 11

thank you!!!!