Particle Models in Two Dimensions
Practice Problems

Problem 1: A shotput is thrown. For the each of the indicated positions of the shotput along its trajectory, draw and label the following vectors: the x-component of the velocity, the y-component of the velocity, and the acceleration. Explain why you drew the vectors as you did.

Problem 1 Solution

Problem 2: A rock is thrown with an initial vertical velocity component of 30 m/s and an initial horizontal velocity component of 40 m/s.

a. What will these velocity components be one second after the rock reaches the top of its path?

b. Assuming the launch and landing heights are the same, how long will the rock be in the air?

c. Assuming the launch and landing heights are the same, how far will the rock land from where it was thrown?

Problem 2 Solution


Problem 3: Two tennis ball launchers shoot balls at the same time, angle and initial speed from different floors of a tall building. The balls land in the street below. Ignore air resistance.

a. Which ball will have the greater acceleration while in flight? Explain your reasoning.

b. Which ball will hit farther from the base of the building? Explain your reasoning.

c. Which ball will reach a greater maximum height? Explain your reasoning.

d. Which ball will be going faster just before hitting the street? Explain your reasoning.

e. How could you adjust only the angle of the upper launcher so that the ball hits in the same place as the ball from the lower launcher? Explain your reasoning.

f. How could you adjust only the angle of the lower launcher so that the ball hits in the same place as the ball from the upper launcher? Explain your reasoning.

Problem 3 Solution

adapted from Qualitative Problems for Introductory Physics by Robert Gibbs


Problem 4: Balls A and B are launched from different heights. The reach the same maximum height at exactly the same point in space.

a. Which ball has a greater initial vertical component of velocity? Explain.

b. Which ball has a greater initial horizontal component of velocity? Explain.

c. Which ball has the larger launch angle? Explain.

d. Which ball has greater acceleration while in flight? Explain.

e. Which ball will land farther from the launchers? Explain.

f. Which ball takes longer to reach maximum height? Explain.

g. If the balls were launched simultaneously, would they collide before landing? Explain.

Problem 4 Solution

adapted from Qualitative Problems for Introductory Physics by Robert Gibbs


Problem 5: If a person can jump a horizontal distance of 3 m on Earth, how far could the person jump on the moon where the acceleration due to gravity is one-sixth of that on earth (1.7 m/s/s)?

Problem 5 Solution


Problem 6: A brick is thrown upward from the top of a building at an angle of 25 degrees above the horizontal and with an initial speed of 15 m/s. If the brick is in the air for 3 seconds, how high is the building? (Draw a picture.)

 Problem 6 Solution


Problem 7: A daredevil tries to jump a canyon of width 10 m. To do so, he drives his motorcycle up an incline sloped at an angle of 15 degrees. What minimum speed is necessary to clear the canyon?

Problem 7 Solution