Myrtle throws a ball upward from a second-floor balcony, 6 m above the ground with an initial velocity of 2 m/s. In this situation, u = 2 and ho = 6, so the relation that models the height of the ball is h = -5t2 + 2t + 6. Myrtle knows that changing the velocity with which she throws the ball will change the maximum height of the ball. Myrtle wants to know with what velocity she must throw the ball to make it pass over a tree that is 11 m tall.

Question

Myrtle throws a ball upward from a second-floor balcony, 6 m above the ground with an initial velocity of 2 m/s.  In this situation, u = 2 and ho = 6, so the relation that models the height of the ball is h = -5t2 + 2t + 6.  Myrtle knows that changing the velocity with which she throws the ball will change the maximum height of the ball.  Myrtle wants to know with what velocity she must throw the ball to make it pass over a tree that is 11 m tall.

a)  Suppose that Myrtle just dropped the ball from the balcony, with an initial velocity of 0 m/s  Write the quadratic relation that models this situation.

b)  What is the maximum height of the ball?

Henry · Answer

V^2 = Vo^2 + 2g*h Vo^2 = V^2-2g*h = 0 + 20*(11-6) = 100 Vo = 10 m/s. To pass over tree. a. 0.5g*t^2 = 6 b. h max = 6 m. = Ht. of balcony.