Question that came up on the test

Question

The following is a question that I confronted on the actual test the other day. Obviously, it is somewhat re-worded, but I am quite certain about the formula and the numbers:

The formula H=-16t^2+vt represents the height at which a ball is thrown in the air. V is the velocity in ft/second and T is the time. If a ball is thrown in the air a velocity of 64 ft/second, how long will it take for the ball to hit the ground? 

Some of the available answer choices included: 8, 16, 32 and 0.

jcgoodchild · Answer

This is a pretty standard physics problem.

The formula H=-16t^2+vt represents the height at which a ball is thrown in the air. V is the velocity in ft/second and T is the time. If a ball is thrown in the air a velocity of 64 ft/second, how long will it take for the ball to hit the ground?

First, we can plug in 64 for v, giving us: H=-16t^2+64t. Now when the ball hits the ground, we know that the height is 0, so we just have to solve the equation for 0. 

0 = -16t^2+64t
16t^2 = 64t
t^2 = 4t
Now, normally we might not be able to do this, but since we know t is NOT 0, we can divide both sides by t. 

therefore, t = 4

Charlie45 · Answer

Thanks for the explanation, that's helpful

ywilfred · Answer

H = -16t^2 + 64t

It hits the ground when h becomes 0.

t(64-16t) = 0
t = 0 (invalid) or t = 64/16 = 16/4 = 4

sm176811 · Answer

Yeah this is a simple Kinematics problem

typically, S=ut + 1/2 a(t^2) where S is the distance, u is the initial velocity, a is the acceleration and t is the time..

In this case S (or H) == 0.

Then you can simply work on the quaratic equation. the values of t should be 0 and some other root.

You will have 2 choose the non zero root.

rao_raghunath · Answer

Good one.. trick is you have to know the height will be zero when it hits ground.

sm176811 · Answer

ywilfred said 

Is NOT invalid. When the object has not left the hand (just when it is launched) t==0.

Charlie45 · Answer

Based on my recent test experience and what I read from others, I feel like they are asking more trick questions like this on the GMAT. Questions in which the calculation might be fairly simple however its a matter of making the connection that the H=0. Some of you might say, well yeah its obvious that H is 0. But in reality, when you are in a test environment and under time pressure, these sort of things might not always come to you as intuitively as you would think. Unfortunately, there is also little preparation one can do for these kind of problems, in some ways they are more like a critical reasoning problem in nature than like the traditional problem solving questions that you see in the official guide.

sm176811 · Answer

I totally agree! And the thing is none of the prep materials - Kaplan, PR, PP, OG have these kind of questions!

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