Proportionality

h = k * v^2

v = 16, h = 4

4 = k * 16^2

k = 4/256

h = 9, v = ?

9 = (4/256) * v^2

9 * 64 = v^2

v = 3 * 8 = 24

bml1105 wrote:The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a max height of 9 feet?



How can you tell which term (16 or 4) is x or y?

Read the question carefully, then decide if your x is velocity or height, y would be height or velocity accordingly.

When two quantities bear direct proportion, their ratio is constant. If v is the velocity with which the object is thrown and h is the maximum height reached by the object thrown directly upward, then we may have

h1/(v1)^2 = h2/(v2)^2.

In the presented question, we numerically have

h1 = 4, v1 = 16, and h2 = 9.

From the relation, we can have

4/(16)^2 = 9/(v2)^2

or (v2)^2 = 9 (16)^2/4, and hence v2 = [spoiler]3 (16)/2 = 24 feet/sec[/spoiler].

bml1105 wrote:The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a max height of 9 feet?

Let h = the maximum height and v = the velocity.

The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown.
Implication:
h�/(v�)² = h₂/(v₂)².

If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a max height of 9 feet?
4/16² = 9/v²
4v² = 16² * 9
v² = 16 * 4 * 9
v = 4 * 2 * 3
v = 24.