On Mars, the gravity acting on an object is less than that on Earth. On Earth, a golf ball hit with an initial upward velocity of 26 meters per second will hit the ground in about 5.4 seconds. The height h of an object on Mars that leaves the ground with an initial velocity of 26 meters per second is given by the equation h = - 1.9t 2 + 26t. How much longer will it take for the golf ball hit on Mars to reach the ground? Round your answer to the nearest tenth.

The answer to the question is

It take for the golf ball hit on Mars to reach the ground 8.284 s longer.

Step-by-step explanation:

To Solve the question, we note that the equation of motion is given to us as

h = - 1.9·t² + 26·t

Therefore the height

We compare the above equation with the equation of of motion

S = ut - 0.5*g*t² where u = initial velocity = 26 m/s and - 0.5*g = - 1.9

Therefore the acceleration due to gravity om mars = - 1.9/-0.5 = 3.8 m/s²

We now have the time taken to maximum height given by

v = u - g·t where v = 0 at maximum height

We therefore have u = g·t → 26 = 3.8*t or t = 26/3.8 = 6.84 seconds

The time taken for ball to hit the ground is 2 * the time to reach maximum height = 2 * 6.84 = 13.684 s

The time longer it takes for the ball on Mars to complete the path up to maximum height and down again is 13.684 s - 5.4 s = 8.284 s.