Question

1. Problem Set B: For each of the following problems, include a sketch of the scenario, name the characteristic the question is asking for and how you will solve for that characteristic. An object is dropped from a bridge over a bay. Its motion is modeled by the quadratic equation h(t) = -16t^2 +56 where t represents the time since the object was dropped and h(t) represents the height of the object. a. How long will it take for the object to reach the water?b. How will you find this characteristic?c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56? a. It takes 56 seconds for the object to reach the ground. b. The object is 56 feet above the ground initially. c. The object reaches its maximum height after 56 seconds.

Answer 1

we have the equation

h(t) = -16t^2 +56

Part a. How long will it take for the object to reach the water?

when the object reach teh water h(t)=0

so

For h(t)=0

solve for t

0=-16t^2+56

16t^2=56

t^2=56/16

t^2=3.5

t=(+/-)1.87

therefore

answer part a is t=1.87 sec

Remember that the time can not be negative

Part b. How will you find this characteristic?

because if the object reach the water is when the height is zero (sea level is the zero)

Part c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56?

answer is

b. The object is 56 feet above the ground initially.