Problema Solution
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 reach a maximum height of about 34.5 meters. 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 = -1.9t2 + 26t. Find the maximum height if the same golf ball is hit on Mars. Round your answer to the nearest tenth.
Answer provided by our tutors
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(t) = -1.9t^2 + 26t
we need to find the maximum of the parabolic function h(t)
the quadratic is in the form y = ax^2 + bx + c with a<0 has maximum equal to y max = c - (b^2)/(4a)
h(t) = -1.9t^2 + 26t has maximum since -1.9 < 0
h max = -0 - (26^2)/(4*(-1.9))
h max = 88.9 m
the maximum height of the golf ball hit on Mars is 88.9 meters.