5. Projectile Motion

Positive (Upward) Launch

Kinematics Part 3: Projectile Motion

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (c) How much time (after it is thrown) is required for the football to return to its original level? How does this compare with the time calculated in part (a)?

In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (a) What is the height of the shelf above the point where the quarter leaves your hand? <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/872d7bc111bea21b-1678205171048.jpg" style="width: 300px;">

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (b) How long does it take the shell to reach its highest point?

 There is not enough information to answer this question. 

Three footballs are punted into the air at <math display="inline"><mrow><mn>32</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mi mathvariant="normal" class="MathML-Unit">m</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow></mrow></math>. Ball A has a launch angle of 34°, Ball B has a launch angle of 41°, Ball C has a launch angle of 57°. Which ball has the longest hang time? In other words, which ball is in the air for the longest time?

In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (b) What is the vertical component of the velocity of the quarter just before it lands in the dish? <img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/6e2e1ded759b37bb-1678205195736.jpg" style="width: 300px;">

A ball is thrown from the top of a 50-m-tall building with a speed of 40 m/s at an angle of 37° above the horizontal. How far horizontally does the ball travel before hitting the ground?

Anderson Video - Projectile Motion Example: Time in Air

Catapult Siege

Projectile Motion Problem

A baseball player hits a pop fly ball. If the ball leaves the bat at <math display="inline"><mrow><mn>45</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mi mathvariant="normal" class="MathML-Unit">m</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow></mrow></math> at an angle of 68° above the horizontal, what is the maximum height, above the point of contact with the bat, that the ball will reach? Ignore air resistance.

A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.0° above the horizontal. The shot hits the ground 2.08 s later. Ignore air resistance. (c) How far did she throw the shot horizontally?

The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0° above the horizontal, some of the tiny critters have reached a maximum height of 58.7 cm above the level ground. (See Nature, Vol. 424, July 31, 2003, p. 509.) (a) What was the takeoff speed for such a leap?

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (b) How high is this point?

Projectile Motion - How Fast When it Hits the Ground | Physics with Professor Matt Anderson | M4-11

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (d) How far from its firing point does the shell land?

Using Single Intervals in Positive Launch Problems

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (d) How far has the football traveled horizontally during this time?

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (a) Find the horizontal and vertical components of the shell’s initial velocity.

A man stands on the roof of a 15.0-m-tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.0° above the horizontal. Ignore air resistance. Calculate (d) Draw x-t, y-t, υx–t, and υy–t graphs for the motion.

A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.0° above the horizontal. The shot hits the ground 2.08 s later. Ignore air resistance. (b) What are the components of the shot’s velocity at the beginning and at the end of its trajectory?

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (c) Find its maximum height above the ground.

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (e) At its highest point, find the horizontal and vertical components of its acceleration and velocity.

You throw a rock off the top of a tall building at an upward angle of 15°. At t=3 s, the rock’s horizontal displacement from you is 52m. How high does the rock get above the top of the building?

Height of a Roof

Solving Non-Symmetrical Upward Launch Problems

Projectile Motion - How Long to Hit the Ground | Physics with Professor Matt Anderson | M4-12

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