# Kinematics question - Rocket launch

In summary, the conversation discusses a homework question about the vertical acceleration and height of a rocket launched from the surface of the Earth. The first 10 seconds of its motion is given by an equation and the task is to find the height at t=10s and the speed when it reaches 200m above the surface. The student attempts to solve the problem but struggles with finding the correct answer. It is suggested to use calculus instead of kinematic equations to solve for the changing acceleration.

Kinematics question -- Rocket launch

## Homework Statement

A rocket starts from rest and moves upward from the surface of the earth. For the first 10s of its motion, the vertical acceleration of the rocket is given by ay=(2.70m/s3)t, where the +y-direction is upward.
A.What is the height of the rocket above the surface of the Earth at t = 10s?
B.What is the speed of the rocket when it is 200m above the surface of the earth?

## Homework Equations

y=y(not)+V(not y)*t-(1/2)*g*t^2
v=V(not y)+a*t

## The Attempt at a Solution

I am stuck on part A and need some help. I used the first equation to find an answer that was wrong. Here is my work:

ay=2.7*(10) =27m/s^3

I then divided that by 9.8 m/s^2 and then multiplied it by 100.

y=0+0-(1/2)*(27/9.8)*(10)^2
y=-860 m
I don't believe the actual answer is going to be negative if the up direction is considered (+). I tried putting (+) 860 in and it said it was wrong. If someone could point me in the right direction for Part A and B that would be much appreciated.

You're given the vertical acceleration of the rocket so it must already take into account all the forces acting, including that due to gravity. Since acceleration is varying over time (it's not constant) you must abandon all your kinematic equations and go back to basics. In other words, a little calculus is called for.

## 1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

## 2. What is a rocket launch?

A rocket launch is the process of sending a spacecraft or missile into space by means of a rocket.

## 3. How is the velocity of a rocket calculated during launch?

The velocity of a rocket during launch is calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity (usually 0), a is the acceleration, and t is the time.

## 4. What factors affect the trajectory of a rocket during launch?

The trajectory of a rocket during launch is affected by factors such as the thrust of the rocket, the mass of the rocket, air resistance, and gravity.

## 5. Can kinematics equations be used to predict the motion of a rocket during launch?

Yes, kinematics equations can be used to predict the motion of a rocket during launch as long as the forces acting on the rocket are known and are constant throughout the launch.