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3. Physics Ex-32 Projectile motion is the vectorial sum of two independent velocities, a horizontal component and a vertical component. The horizontal component velocity (V H ) is constant throughout the motion while the vertical component velocity (V V ) 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 velocities separately as if they were two separate problems. Click N O T E

5. Physics Ex-32 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) Click 0 10 20 30 40 50 0 25 10 25 20 25 30 25 40 25 50 Use 10 m/s 2 for the acceleration due to gravity. Click

6. Physics Ex-32 Question-2 Click A stone is dropped from a balcony 20 m high. How long does it take the stone to reach the ground?

7. Physics Ex-32 Question-3 Click 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. Click Step-1: Calculation of falling time Step-2: Calculation of range Click

8. Physics Ex-32 Question-4 Click A ball is thrown in the air with a velocity of 20 m/s at an angle of 60 o from the horizontal. Calculate: NOTE The vertical component of the velocity is identical to shooting an object vertically upwards. a) How high it rises (the height).

9. Physics Ex-32 Question-4 Click A ball is thrown in the air with a velocity of 20 m/s at an angle of 60 o from the horizontal. Calculate: NOTE The horizontal component of the velocity is the same throughout the flight and is thus an average velocity. b) How far it travels (the range). Multiply by 2 to obtain total time.

10. Physics Ex-32 Question-5 Click A ball is thrown in the air with a velocity of 20 m/s at an angle of 45 o from the horizontal. Calculate: NOTE The vertical component of the velocity is identical to shooting an object vertically upwards. a) How high it rises (the height). Click

11. Physics Ex-32 Question-5 Click A ball is thrown in the air with a velocity of 20 m/s at an angle of 45 o 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. Multiply by 2 to obtain total time. Click

12. Physics Ex-32 Question-6 Click A ball is thrown in the air with a velocity of 20 m/s at an angle of 30 o from the horizontal. Calculate: NOTE The vertical component of the velocity is identical to shooting an object vertically upwards. a) How high it rises (the height).

13. Physics Ex-32 Question-6 Click A ball is thrown in the air with a velocity of 20 m/s at an angle of 30 o 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.

14. Physics Ex-32 Question-7 Click The table below summarizes the answers from the previous three questions (4, 5 and 6): Initial velocityAngleHeightRange Question-420 m/s60 o 15 m35 m Question-520 m/s45 o 10 m40 m Question-620 m/s30 o 5 m35 m Which angle produces the greatest height? a) 60 o Which angle produces the greatest range? b) 45 o Click REMEMBER The greatest range is always produced by an angle of 45 o.

15. Physics Ex-32 Question-8 Click A cannon ball is fired into the air at an angle of 40 o from the horizontal and rises 5 m. Calculate its range. Click Time = 1 s going up + 1 s coming down

16. Physics Ex-32 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 30 o above the horizontal, calculate how far from the base of the cliff the ball hits the ground. Question-9 Click

17. Physics Ex-32 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 30 o below the horizontal, calculate how far from the base of the cliff the ball hits the ground. Question-10 Click

18. Physics Ex-32 Question-11 Click 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 the projectile. Answer: 21.9 m/s [E 45 o N]

19. Physics Ex-32 Question-12 Click 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: The time it takes the projectile to hit the ground. a) Click

20. Physics Ex-32 Question-12 Click 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: The horizontal displacement. b) Click

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