An object is launched at 20 m/s from a height of 65 m. the equation for the height (h) in terms of time (t) is given by h(t) = -4.9t² + 20t + 65. what is the object's maximum height? the numeric answer only, rounded to the nearest meter.

Maximum height will be 85 meter

Explanation:

given that height of an object is function of time and it is given as

here we can write it as

now we can compare it with the kinematics equation

now if we compare the two equations then we will have

initial height of object = 65 m

initial velocity of projection = 20 m/s

acceleration = - 9.8 m/s/s

now for the maximum height at which its final speed will become zero is given as

So maximum height in meter in nearest integer will be 85 m

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts