Projectile Motion:- Equation 2: v2 = u2 + 2as

This is an example worksheet with worked solutions to be used with the regenerating worksheets "Equation2".


Q.2. Jack dropped a stone from a balcony and it hit the ground at 19 m/s. How high was the balcony ?

Q.3. Leo dropped a spanner from the top of the Watchamacallit Bridge. How fast was it travelling as it hit the water 61 m below?

Q.4. Cate threw a stone vertically down from the top of a cliff with an initial speed of 7 m/s. How fast was it going as it hit the ground 49 m below?

Q.5. Lisa threw a stone vertically up from a cliff top at 12 m/s. The stone slowed as it went up and stopped momentarily, and then gradually increased speed until it hit the ground at the bottom of the cliff 58 m below. How fast was the stone travelling as it hit the ground?

Q.6. Kayley threw a ball vertically down from a balcony and it hit the ground 42 m below at 35 m/s. What was the speed with which Kayley threw the ball down?

Q.7. Vateesh placed an orange on the edge of a coffee table that was 64 cm high. If the orange rolled off the edge of the table, how fast would it be going when it hit the floor?

Q.8. Nathan dropped a water balloon from a balcony and it hit Leah, who was standing below, with a speed of 49 m/s. How far did the balloon fall?

Q9. Ben dropped a spanner from the Moon lander and it fell to the surface of the Moon 1.0 m below. If the acceleration due to gravity on the Moon is 1.6 m/s/s. How fast was the spanner travelling as it hit the Moon's surface? " + "

Q10. A scientist on the newly discovered planet Seitsew fired a rocket vertically upwards with a velocity of 34 m/s. The rocket reached its maximum height of 158 metres.
What is the value of g, the acceleration due to gravity, on Seitsew?


Answers:

Q.1. Taylah dropped a ball from a roof that was 11 m high. How fast was the ball travelling when it hit the ground?

v2 = u2 + 2as
v2 = 02 + 2 x 9.8 x 11
v2 = 215.6
v = √215.6 = 14.68 m/s

Q.2. Jack dropped a stone from a balcony and it hit the ground at 19 m/s. How high was the balcony ?

v2 = u2 + 2as
192 = 02 + 2 x 9.8 x s
361 = 19.6s
s = 361/19.6 = 18.42m

Q.3. Leo dropped a spanner from the top of the Watchamacallit Bridge. How fast was it travelling as it hit the water 61 m below?

v2 = u2 + 2as
v2 = 22 + 2 x 9.8 x 61
v2 = 1195.6
v = √1195.6 = 34.58m/s

Q.4. Cate threw a stone vertically down from the top of a cliff with an initial speed of 7 m/s. How fast was it going as it hit the ground 49 m below?

v2 = u2 + 2as
v2 = 72 + 2 x 9.8 x 49
v2 = 49 + 960.4 = 1009.4
v = √1009.4 = 31.77m/s

Q.5. Lisa threw a stone vertically up from a cliff top at 12 m/s. The stone slowed as it went up and stopped momentarily, and then gradually increased speed until it hit the ground at the bottom of the cliff 58 m below. How fast was the stone travelling as it hit the ground?

v2 = u2 + 2as
v2 = (-12)2 + 2 x 9.8 x 58 (note that the initial velocity and gravity have opposite signs since they are in opposite directions.)
v2 = 144 + 2 x 9.8 x 58
v2 = 1280.8
v = √1280.8 = 35.79m/s

Q.6. Kayley threw a ball vertically down from a balcony and it hit the ground 42 m below at 35 m/s. What was the speed with which Kayley threw the ball down?

v2 = u2 + 2as
352 = u2 + 2 x 9.8 x 42
1225 = u2 + 823.2
u2 = 1225 - 823.2 = 401.8
u = √401.8 = 20.04m/s

Q.7. Vateesh placed an orange on the edge of a coffee table that was 64 cm high. If the orange rolled off the edge of the table, how fast would it be going when it hit the floor?

v2 = u2 + 2as
v2 = 02 + 2 x 9.8 x 0.64
v2 = 12.544
v = √12.544 = 3.54m/s

Q.8. Nathan dropped a water balloon from a balcony and it hit Leah, who was standing below, with a speed of 49 m/s. How far did the balloon fall?

v2 = u2 + 2as
492 = 02 + 2 x 9.8 x s
2401 = 19.6s
s = 2401/19.6 = 122.5m


Q9. Ben dropped a spanner from the Moon lander and it fell to the surface of the Moon 1.0 m below. If the acceleration due to gravity on the Moon is 1.6 m/s/s. How fast was the spanner travelling as it hit the Moon's surface? " + "

v2 = u2 + 2as
v2 = 02 + 2 x 1.6 x 1.0
v2 = 3.2
v = √3.2 = 1.789m/s = 1.79m/s (2 d.p.)

Q10. A scientist on the newly discovered planet Seitsew fired a rocket vertically upwards with a velocity of 34 m/s. The rocket reached its maximum height of 158 metres.
What is the value of g, the acceleration due to gravity, on Seitsew?

v2 = u2 + 2as
02 = (-34)2 + 2 x g x 158
- 1156 = 316g g = -1156/316 = 3.65823 = -3.66 m/s/s (2 d.p.)
The negative sign for gravity means that it is in the opposite direction to the direction the rocket was fired.