How Do You Calculate the Acceleration Due to Gravity on an Unknown Planet?

[Melchior25]

You land on an unknown planet somewhere in the universe that clearly has weaker gravity than Earth. To measure g on this planet you do the following experiment: A ball is thrown upward from the ground. It passes a windowsill 15.0 m above ground and is seen to pass by the same windowsill 2.00 s after it went by on its way up. It reaches the ground again 5.00 s after it was thrown. Calculate the magnitude of g (the acceleration due to gravity) at the surface of this planet.

I drew the picture and started to sole the problem this way but I keep getting the wrong answers. Any input would be greatly appreciated.

to me the initial velocity after 2 seconds should be
v=distance/time which is 15m/2sec so the initial velocity should be 7.5m/s at that point. So from here I used

xf=1/2at^2+vit+xi

15=1/2a(2)^2+(7.5)(2)+0

a=-7.5

I get a gravitational acceleration of -7.5m/s^2. I tried 7 a well thinking the magnitude would be positive. But both answers are wrong.

 

[Shooting Star]

to me the initial velocity after 2 seconds should be
v=distance/time which is 15m/2sec so the initial velocity should be 7.5m/s at that point.

The particle is undergoing accn; it's not traveling at a uniform velo. What you have used is valid if speed is const. Correct it.

EDIT:

After another read, it's never even said anywhere that it took 2 secs to travel 15 m. It crossed the window sill at t=t' traveling up and t=t'+5 going down.

Use the eqns for motion under unifrom accn.