MATH SOLVE

3 months ago

Q:
# A rock is thrown upward with an initial velocity of 122 feet per second. The height of the rock ,(h), in feet after t seconds is given by the function ℎ() = −162 + 122 + 10.How long does it take the rock to reach its maximum height? What is the rock’s maximum height. Round to the nearest hundredth, if necessary.

Accepted Solution

A:

Answer: the maximum height is 231.118 feetStep-by-step explanation:Initial velocity, u = 122 feet per second. The height of the rock ,(h), in feet after t seconds is given by the function ℎ(t) = −162x^2 + 122x + 10.Acceleration of the object is 32.17405 ft/s2. This is approximately 32.2 ft/s2. It is same as the acceleration due to gravity. Since the object is moving upwards, the acceleration will be negative because it is moving in the opposite direction of the gravitational force.Thereforeg = - 32.2 ft/s^2The final velocity, v = 0 at maximum height.Applying Newton's equation of motion,v^2 = u^2 + 2gh0 = 122^2 + (-32.2 × 2 ×h)0 = 14884 - 64.4h64.4h = 14884h = 14884/64.4 = 231.118 feets( approximated to the nearest hundredth)