Axis Kinematic

Kinematics Problem? A rocket, initially at rest, is fired vertically with an upward acceleration of 10.0 m/s^2?

A rocket, initially at rest, is fired vertically, with an upward acceleration of 10.0 m/s^2. At an altitude of 0.78km (780 m), the engine of the rocket cuts off. What is the maximum altitude it achieves?

I know you use the kinematic equations for one dimension along the y-axis:

V_y=V_oy-gt
Y=V_oyt-.5gt^2

But I don't know how to solve the problem without V_oy (initial velocity) or V_y given..

Can someone explain how to solve this problem?

The phrase "initially at rest" tells you that V_oy is zero at the start of the sequence.

While the engine is producing acceleration:

Y = .5*a*t^2 = 780 = .5*10*t^2

t^2 = 780/5 = 156

t = 12.49 seconds

The velocity is then:

V_y = a*t = 10*12.49 = 124.9 m/s

This becomes the V_oy for the coasting part of the sequence. The maximum altitude occurs when V_y = 0

V_y = 0 = 124.9 - 9.8*t

-124.9/-9.8 = t = 12.745 seconds coasting to altitude

Y = 780 + 124.9*12.745 - .5*9.8*(12.745)^2 = 1575.9m

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What torque will bring the balls to a halt in 5.0 s?

A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm.

What torque will bring the balls to a halt in 5.0 s?

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I just can't get this. I know that I have to use torque = angular acceleration* moment of inertia

I can get the angular acceleration in radians per second from kinematic equations for rotational motion. Calculating the moment of inertia is the only trouble I'm having. Please help. Im trying to use the parallel axis theorem too but nothing works.

the speed of the center will hold any thing in place f/grav at speed