You\'re analyzing measurements taken on a planet where the gravitational force i

Question

You're analyzing measurements taken on a planet where the gravitational force is different than that of Earth. In one experiment, the exploring astronauts dropped a small mass off the top of a boulder (v_0=0 m/s). They released the mass at a height H= 10 m above the surface of the planet. The mass hit the ground 1.8 seconds after it is dropped and has a velocity Vi on impact. (Neglect the other planets air resistance.) What is the acceleration due to gravity on the planet?. In a long-term colony on the new planet, people will want to play sports. If Peyton Manning throws a football at a speed of 29 m/s at a horizontal angle of 30 degrees, how far and how high does he throw the ball on this new planet?T4ow does this compare to what he can do on Earth if he throws the ball at the same speed and angle?

Explanation / Answer

As equation of motion is S= ut+ 1/2at2. S is 10m, t = 1.8 sec. Acceleration will due to gravity at that planet, hence a= 2S/t square i.e. 6.172m/sec square.

Horizontal range for football will be = horizontal velocity× time of flight. i.e. ucos$ × 2usin$ / g at that planet. Hence football will go 118m away.

The maximum height will be u square sin square $ / 2g at that planet. Hence football will go up to height 17.03m.

On earth g will be 9.81, hence horizontal range will be 74.24m.

And maximum height would be 10.71m.

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