Conceptual Physics

Step-by-step solution

We start by calculating the vertical component of the initial velocity. We use the fact that gravity will slow the ball to a vertical velocity of 0 m/s

at the peak, 0.60 seconds (halfway) into the flight.

Now we solve for the horizontal velocity component. We could have solved for this first; these steps require no results from the steps above.

From our perspective, the horizontal velocity of the ball when it is going from our left to our right is positive. From the juggler’s, it is negative.

Step Reason

1. vyf = vyi + ayt motion equation

2. 0 = vyi + ayt vertical velocity at peak equals zero

3. vyi = –ayt rearrange

4. vyi = í(í9.80 m/s^2 )(0.600 s) enter values

5. vyi = 5.89 m/s multiply

Step Reason

6. definition of velocity

7. enter values

8. vx = 0.625 m/s divide

4.9 - Interactive problem: the monkey and the professor, part II

The monkey is at it again with his banana bazooka. Another hungry professor drops

from the tree the instant the banana leaves the tip of the bazooka. (Are professors

paid enough? Answer: No.)

Can you correctly aim the banana so that it hits the professor’s glove as she falls?

Should you aim the shot above, below or directly at the glove? Does the banana’s

initial speed matter? (Note: The simulation has a minimum speed so the banana will

reach the professor when correctly aimed.) Air resistance is ignored in this

simulation.

Give it a try in the interactive simulation to the right. No calculations are needed to

solve this problem.

To find an answer, think about the key concepts of projectile motion: Objects

accelerate toward the ground at the same rate, and the horizontal and vertical

components of motion are independent.

Once you launch the simulation, aim the banana by dragging the vector arrow at the

end of the bazooka. You can increase the firing speed of the banana by making the

arrow longer. Moving the arrow up or down changes the angle at which the banana is fired. Stretching out the vector makes it easy to aim the

banana.

To shoot the banana, press GO. Press RESET to try again. Keep trying until the banana reaches the professor!

(^74) Copyright 2000-2007 Kinetic Books Co. Chapter 04