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Projectile Motion: Solving Problems with Vertical and Horizontal Velocities

This exercise focuses on projectile motion, which involves the vectorial sum of horizontal and vertical velocities. Learn how to calculate velocities and solve problems related to projectile motion with step-by-step explanations and practice exercises.

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Projectile Motion: Solving Problems with Vertical and Horizontal Velocities

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  1. High School PHYSICS InClass by SSL Technologies with S. Lancione Exercise-32 Projectile Motion

  2. NOTE Projectile motion is the vectorial sum of two independent velocities, a horizontal component and a vertical component. The horizontal component velocity (VH) is constant throughout the motion while the vertical component velocity (VV) equals free fall. The actual or instantaneous velocity at any point along the parabolic path is tangent to the parabola and equal to the vectorial sum of the horizontal and vertical component velocities. In solving problems on projectile motion, work out the vertical and horizontal component velocitiesseparatelyas if they were two separate problems. Projectile Motion Click Click

  3. EXERCISES

  4. Question-1 Two stones, A and B, are used in an experiment. At the same time that stone A is dropped, stone B is thrown down horizontally with a velocity of 25 m/s. For each second of fall, fill in the velocities of both stones, as indicated. (You need not include the units) 0 10 25 0 25 10 20 25 20 Use 10 m/s2 for the acceleration due to gravity. 30 25 30 40 25 40 50 25 50 Click Click

  5. Question-2 A stone is dropped from a balcony 20 m high. How long does it take the stone to reach the ground? Answer Click Click

  6. Question-3 A ball is thrown horizontally from a 20 m high cliff with a velocity of 10 m/s. How far from the base of the cliff does the ball land? NOTE The time it takes the ball to strike the ground is the same time it takes an object to fall freely 20 m. Step-1: Calculation of falling time Answer Step-2: Calculation of range Click Click Click

  7. Question-4 A ball is thrown in the air with a velocity of 20 m/s at an angle of 60o from the horizontal. Calculate: a) How high it rises (the height). NOTE The vertical component of the velocity is identical to shooting an object vertically upwards. Click Click

  8. Question-4 Multiply by 2 to obtain total time. A ball is thrown in the air with a velocity of 20 m/s at an angle of 60o from the horizontal. Calculate: b) How far it travels (the range). NOTE The horizontal component of the velocity is the same throughout the flight and is thus an average velocity. Answer Click Click

  9. Question-5 A ball is thrown in the air with a velocity of 20 m/s at an angle of 45o from the horizontal. Calculate: a) How high it rises (the height). NOTE The vertical component of the velocity is identical to shooting an object vertically upwards. Answer Click Click Click

  10. Question-5 Multiply by 2 to obtain total time. A ball is thrown in the air with a velocity of 20 m/s at an angle of 45o from the horizontal. Calculate: b) How far it travels (the range). NOTE The horizontal component of the velocity is the same throughout the flight and is thus an average velocity. Answer Click Click Click

  11. Question-6 A ball is thrown in the air with a velocity of 20 m/s at an angle of 30o from the horizontal. Calculate: a) How high it rises (the height). NOTE The vertical component of the velocity is identical to shooting an object vertically upwards. Answer Click Click

  12. Question-6 A ball is thrown in the air with a velocity of 20 m/s at an angle of 30o from the horizontal. Calculate: b) How far it travels (the range). NOTE The horizontal component of the velocity is the same throughout the flight and is thus an average velocity. Answer Click Click

  13. Question-7 The table below summarizes the answers from the previous three questions (4, 5 and 6): REMEMBERThe greatest range is always produced by an angle of 45o. a) Which angle produces the greatest height? 60o b) Which angle produces the greatest range? 45o Click Click Click

  14. Question-8 Time = 1 s going up + 1 s coming down A cannon ball is fired into the air at an angle of 40o from the horizontal and rises 5 m. Calculate its range. Answer Click Click

  15. Question-9 A ball is thrown into the air from a cliff 20 m high. If the ball is thrown with a velocity of 15 m/s at an angle of 30oabove the horizontal, calculate how far from the base of the cliff the ball hits the ground. Answer Click Click

  16. Question-10 A ball is thrown into the air from a cliff 20 m high. If the ball is thrown with a velocity of 15 m/s at an angle of 30obelowthe horizontal, calculate how far from the base of the cliff the ball hits the ground. Answer Click Click Click Click

  17. Question-11 A projectile is fired into the air with such initial velocity that its height is 12 m and its range is 48 m. Determine the initial velocity of theprojectile. Answer: 21.9 m/s [E 45o N] Click Click

  18. Question-12 A helicopter is rising vertically at 15 m/s. When it is at a height of 200 m above the ground, it fires a projectile horizontally with a velocity of 50 m/s. Determine: a) The time it takes the projectile to hit the ground. Answer Click Click Click

  19. Question-12 A helicopter is rising vertically at 15 m/s. When it is at a height of 200 m above the ground, it fires a projectile horizontally with a velocity of 50 m/s. Determine: b) The horizontal displacement. Answer Click Click

  20. SSLTechnologies.com/science The end

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