Please help me.

Question

1. A projectile that is fired vertically into the air with an initial velocity of 16 meters per second can be modelled by the equation h = 15t - t ^ 2 . In the equation, h is the height in meters of the projectile above the ground after t seconds.

a. What is the maximum height of the fired projectile above the ground?

b. At how many seconds will the projectile reach the maximum height?

2. The perimeter of a rectangular field is 120 meters.

a. What is the maximum area of the rectangular field?

b. What are the dimensions of the field such that you will get the maximum area?

Answer 1

h(t) = 15t - t^2 is what you say is the model, but if the initial velocity is 16 meters per second the model for a projectile shot at sea level would be h(t) = 16t - 4.9t^2

using your model, take the derivative and set = 0, to get h'(t) =15-2t = 0, where t =15/2 = 7.5 seconds to reach maximum height. Maximum height is h(7.5) = 15(15/2) - (15/2)^2 = 225/4 = 56 1/4 meters

using the usual model h'(t) = 16t-4.9t^2, h'(t) = 16 - 9.8t = 0, with t = 16/9.8 seconds for max height

h(16/9.8) = 16(16/9.8) - 9.8(16./9.8 = 6.2(16)/9.8 = about 10.12 meters = max height in about 1.63 seconds

Perimeter = 120 = 2(L+W)

L+W = 60 meters, L=60-W

Area = LW= (60-W)W = 60W -W^2

A' = 60-2W = 0

W =60/2 = 30 meters

L = 30 meters

Maximum Area is when the rectangle is a square