Projectile Motion, finding g on a planet

[steph35]

Homework Statement

An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 10.0 m if her initial speed is 2.40 m/s.

Homework Equations

What is the free-fall acceleration on the planet? (Ignore air resistance.)

The Attempt at a Solution

So in order to this I used both position functions in the x and y directions to get. x_f= 2.40(cos45)t and y_f= 2.40(sin45)t-(1/2)gt^2. i solved for t to get the time which is t= 5.89 seconds. and then now i know i have to find y_f so then i can plug it in and find g! but how am i supposed to find y_f without a equation that is also dependent on g?

 

[tiny-tim]

Hi steph35!

An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 10.0 m if her initial speed is 2.40 m/s.
…
but how am i supposed to find y_f … ?

erm … it's obvious what y_f is … it's given in the question, isn't it?

 

[baba89]

To find the free-fall acceleration on the planet, we can use the equation y_f = y_i + v_iy*t + (1/2)gt^2, where y_i is the initial height (in this case, the height of the astronaut when she starts her jump), v_iy is the initial velocity in the y-direction (in this case, 2.40*sin45), and t is the time calculated in your attempt. By substituting these values and solving for g, we can find the free-fall acceleration on the planet. It is important to note that the value of g may be different on this planet compared to Earth, as it depends on the mass and radius of the planet.