You have probably heard about all of the exoplanets (planets outside our solar s

Question

You have probably heard about all of the exoplanets (planets outside our solar system) being discovered lately. On a planet far, far away, Luke tosses a ball into the air. Some time later, the ball's velocity components are 10.0 m/s horizontally, and 8.0 m/s up. 3.0 seconds after that, the ball?s velocity components are 10.0 m/s horizontally, and 7.0 m/s down. [2 points] (a) What is the value of g on this planet? [2 points] (b) The ball lands at the same level it was launched from, spending a total time of 10 s in the air. Calculate the components of the ball?s initial velocity. [4 points] (c) On the graph below (note that it is y vs. x, not versus time) do three things: - Place a dot at the origin. Then, on the x-axis, draw dots at the locations of the ball?s x-position, for t 1 s, 2 s, 3 s, etc. (every second until the ball lands); - On the y-axis, draw dots at the locations of the ball?s y-position, for t = 1 s, 2 s, 3 s, etc. (every second until the ball lands). - Use those dots to help you draw dots at the ball?s actual location, for t = 1 s, 2 s, 3 s, etc. (every second until the ball lands).

Explanation / Answer

Balls horizontal velocity do not changes thus only vertical acceleration

vfy=viy+a*t

-7=8+a*3       => a=-5 m/s2

thus the acceleration is vertically downward

Ball required t=(10/2)=5s to take max height

at Hmax

Vfy=0m/s

Vfy=Viy+a*t

0=Viy-5*5      =>Viy= 25m/s

Vix is given = 10m/s

Thus Vi= sqrt(vix^2+Viy^2)= sqrt(10^2+25^2) = 26.93 m/s

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