Question

HELP

2 + vt + s to answer the question.

A juggler throws a ball from an initial height of 4 feet with a velocity of 30 feet per second. If the
juggler misses the ball, after how many seconds does it hit the ground? Show all work.

13) Use the vertical motion model h = -16t

2 + vt + s to answer the question.

A hawk, flying at a height of 50 feet, spots a rat on the ground. If he dives down to catch the rat at
a speed of 45 feet per second, how long will it take him to catch the rat?

Answer 1

The ball hits the ground after approximately 0.5 seconds.

Step-by-step explanation:

To solve this problem, we can use the vertical motion model, which is represented by the equation h = -16t^2 + vt + s. In this case, the initial height (s) is 4 feet and the velocity (v) is 30 feet per second.

Setting h = 0, we can solve for t to find when the ball hits the ground:

0 = -16t^2 + 30t + 4

Using the quadratic formula, t = (-b ± √(b^2 - 4ac)) / 2a, where a = -16, b = 30, and c = 4:

t = (-30 ± √(30^2 - 4(-16)(4))) / (2(-16))

t = (-30 ± √(900 + 256)) / -32

t = (-30 ± √1156) / -32

t = (-30 ± 34) / -32 --> t = 1/2 or t = -17/16

Since time cannot be negative, the ball hits the ground after approximately 0.5 seconds.

Answer 2

Answer: For the equation simply substitute 30 in for v and 4 in for s in the equation given, so H=-16t^2+30t+4

Part 2.

If the juggler misses the ball, you wish to know the time that it takes for the ball to travel the four feet from his hand to the ground, so respectively,

4=-16t^2+30t+4 or 0=-16t^2+30t or 0 = -16t+30,

solving for t, t =30/16 seconds or 1.875 seconds

Step-by-step explanation: