2 A stone is thrown straight down from the edge of a roof 70

2)

A stone is thrown straight down from the edge of a roof, 700 feet above the ground at a speed of 5 feet per second. Remembering that the acceleration due to gravity is -32 feet per second squared, is the stone 3 seconds later? At what times does the stone hit the ground? What is the velocity of the stone when it hits the ground? A stone is dropped from the edge of roof, and hits the ground with a velocity feet per second How high ( in feet ) is the roof?

Solution

upward direction has been taken as +ve. easiest is to use the appropriate SUVAT equations a. s = 700 + ut + 0.5at^2 = 700 - 5*3 - 0.5*32*9 = 541 ft <------ b. when the stone hits the ground, 5=0; so set 5=0 and solve the quadratic: 0 = 700 - 5t - 16t^2, solving the quadratic & taking +ve value, t = 6.459 s <------- c. the speed as a function of time is v(t) = v0 + at v = u + at = -5 - 32*6.459 = -211.69 ft/s <-------