Determine the acceleration due to gravity on this planet

darbeecakes

1. Homework Statement
A projectile is launched over level ground on an unnamed planet. The equation of the projectile's vertical position is y(t)=-6t2+48t-90.
a. Determine the acceleration due to gravity on this planet
b. Determine (ymax, tymax), the coordinates of the maximum height of the projectile in the t-y plane

2. Homework Equations
rf=ri+vit+1/2gt2

3. The Attempt at a Solution
I know ri=0 because that's the origin
Since I'm not given a time or velocity I'm stuck on how to solve for anything

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ehild

Homework Helper
1. Homework Statement
A projectile is launched over level ground on an unnamed planet. The equation of the projectile's vertical position is y(t)=-6t2+48t-90.

2. Homework Equations
rf=ri+vit+1/2gt2

3. The Attempt at a Solution
I know ri=0 because that's the origin
Since I'm not given a time or velocity I'm stuck on how to solve for anything
Write y and yi in your equation instead of r and ri. The equation given and your one should be equivalent, that is they have to give the same y at every time t. What does it mean for yi, vi and g?

ehild

darbeecakes

Thank you. yi is the initial y position, vi is the initial velocity, and g is gravity due to acceleration.

ehild

Homework Helper
Thank you. yi is the initial y position, vi is the initial velocity, and g is gravity due to acceleration.
Compare it with the original equation
y(t)=-6t2+48t-90

What is the value of the initial position, initial velocity and acceleration?

ehild

darbeecakes

So the initial position is -90, initial velocity is 48t and acceleration is -6t2?

ehild

Homework Helper
t is the running time. Anything that contains t changes with time. The initial velocity is the velocity at t=0.

ehild

darbeecakes

So do I leave the acceleration value as -6t2 or do I solve it further by substituting a value for t? And how do I find the final t value?

ehild

Homework Helper
You have the general equation for the vertical position of a projectile

y(t)=yi+vit -g/2 t^2

(assuming that the positive y axis points upward and vi is the initial upward velocity).

On that planet, you launch a projectile upward from a valley and you get the vertical position as function of time:

y(t)=-90 +48t -6t2.

These equations should be equivalent, the positions y(t) given by both equations are the same at any time. You certainly have learnt that the coefficients of two polynomials have to agree pairwise in order they are equivalent. The coefficients of t^2 in both equations have to be the same: so -g/2=-6. The coefficient of t should agree, too, so 48=vi.

ehild

darbeecakes

How do I find the coordinates for the maximum height of the projectile?

ehild

Homework Helper
How can you find the maximum of a function?

ehild

darbeecakes

I know the equation for the maximum height is the same as the first one i gave with ymax substituted in for rfinal and yinitial substituted in for rinitial, but I'm not sure how to find coordinate numbers when two variables are unknown.

ehild

Homework Helper
You should calculate the maximum height and the time the projectile reaches it. If you studied calculus you know that the maximum of y is at that value of t where the derivative of y with respect to t is zero: dy/dt=0.
The other approach: you know that the vertical velocity of a projectile is v=vi-gt. You can find the rise time from the condition v=0.

ehild

darbeecakes

I ended up getting t=4 and y=6.
I think it's correct.
Thank you for the help.

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