Question 46
A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation below. How long will it take the rock to reach the river?
h=-16t^2+320
a, 2.5 seconds
b. 3.5 seconds
c. 3.8 seconds
d. 4.5 seconds
To find the time it will take for the rock to reach the river, we need to set h (height) equal to 0, since the rock will reach the river when its height is 0.
So we have:
0 = -16t^2 + 320
Solving for t:
16t^2 = 320
t^2 = 20
t = √20
t ≈ 4.5 seconds
Therefore, the rock will take 4.5 seconds to reach the river, so the answer is d) 4.5 seconds.
Question 45
April shoots an arrow upward at a speed of 80 feet per second from a platform 25 feet high. The pathway of the arrow can be represented by the equation below, where "h" is the height and "t" is the time in seconds. What is the maximum height of the arrow?
h=-16t^2+80t+25
a. 80 feet
b. 90 feet
c. 125 feet
d. 140 feet
The maximum height of the arrow can be found by determining the vertex of the parabola given by the equation.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula:
x = -b / 2a
For the equation h = -16t^2 + 80t + 25:
a = -16
b = 80
Substitute these values into the formula:
t = -80 / (2*(-16))
t = -80 / (-32)
t = 2.5 seconds
To find the maximum height, substitute t = 2.5 back into the equation:
h = -16(2.5)^2 + 80(2.5) + 25
h = -16(6.25) + 200 + 25
h = -100 + 200 + 25
h = 125 feet
Therefore, the maximum height of the arrow is 125 feet, so the answer is c) 125 feet.