Question

An object is propelled vertically upward with an initial velocity of 20 meters per second. The distance (in meters) of the object from the ground after seconds is

(a) When will the object be 15 meters above the ground?
(b) When will it strike the ground?
(c) Will the object reach a height of 100 meters?

Answer 1

To find the distance of an object from the ground after a certain amount of time when propelled vertically upward, we can use the kinematic equation. In this problem, we determined when the object will be 15 meters above the ground, when it will strike the ground, and if it will reach a height of 100 meters.

Step-by-step explanation:

In this problem, we are given an object that is propelled vertically upward with an initial velocity of 20 meters per second. To solve for the distance of the object from the ground after a certain amount of time, we can use the kinematic equation:

Distance = Initial velocity * time - 0.5 * acceleration * time^2

(a) To find when the object will be 15 meters above the ground, we can set the distance equal to 15 and solve for time:

15 = 20t - 0.5 * 9.8 * t^2

Using the quadratic formula, we find that the object will be 15 meters above the ground after approximately 1.29 seconds.

(b) To find when the object will strike the ground, we need to find the time at which the distance is 0:

0 = 20t - 0.5 * 9.8 * t^2

Solving this equation, we find that the object will strike the ground after approximately 4.08 seconds.

(c) To determine if the object will reach a height of 100 meters, we can set the distance equal to 100 and solve for time:

100 = 20t - 0.5 * 9.8 * t^2

Using the quadratic formula, we find that the object will reach a height of 100 meters after approximately 10.10 seconds. Therefore, the object will not reach a height of 100 meters.