Peter is snowbaording and goes off a 10 foot incline at 60 f

Peter is snowbaording and goes off a 10 foot incline at 60 feet per second. The equation for peter\'s height is h(t)= -16t^2 + 60t + 10 where h(t) is height and t is time. What is the highest that peter will be in feet? What is the time that it will take Peter to reach his highest point? Find out how long it will take for peter to land?

Solution

At max height, h\'(t)=0

=> -32t+60=0

=> t=60/32=1.875

Therefore, max. height=-16(1.875)^2 + 60(1.875) + 10 = 66.25

When Peter will reach land, h(t)=0

=> -16t^2+60t+10=0

=> t=-0.16 or 3.91

Since time cannot be negative, therefore t=3.91