Projectile Motion:- Equation 3: s = ut + ½ at2

Q.1. Taylah dropped a ball from a balcony and it took 4s to hit the ground. How high was the balcony?

Q.2. Jack dropped a stone from a cliff on Mars where the acceleration due to gravity is 3.3 m/s/s. The stone took 7seconds to hit the ground. How high was the cliff?

Q.3. Nathan dropped a water bomb from a stationary hot-air balloon that was 49m above Leah's head. How long did the water bomb take to fall from the balloon and burst on Leah's head?

Q.4. Cate threw a stone vertically down from the roof of a tall building with an initial speed of 7m/s and it took 6 seconds to hit the ground below. How tall was the building?

Q5. Adam threw a stone vertically upwards. The stone slowed as it went up and stopped momentarily, then gradually increased speed as it fell until it hit the ground 3 seconds after throwing. What was the maximum height reached by the stone?

Q.6. Lisa threw a stone vertically down from a cliff on the Moon at 17m/s where the acceleration due to gravity is 1.7m/s/s. The stone hit the ground at the bottom of the cliff 5 seconds later. How high was the cliff?

Q7. Antonia threw a ball vertically down from a balcony of a very tall building. The ball hit the ground 1192.5 m below 15 seconds later. What was the speed with which the ball was thrown?

Q8. Samantha was in the basket of a hot-air balloon that was travelling upwards with a constant speed of 17 m/s. She held a water-bomb over the side of the basket and when the basket was a distance d above Chris's head she released the water bomb. The water-bomb hit Chris on the head 13 seconds later.
How far above Chris's head was the water bomb when it was released?

Q9. Pat had a hole in his pocket and a coin slipped out. How long would it take the coin to hit the floor 81 cm below?

Q10. A scientist on the newly discovered planet Eidum fired a projectile vertically upwards The projectile reached its maximum height of 354m 20 seconds later. What is the value of g, the acceleration due to gravity, on Eidum?

Answers:

Q.1. Taylah dropped a ball from a balcony and it took 4s to hit the ground. How high was the balcony?

s = ut + ½ at2
If the ball is dropped rather than thrown down, the initial velocity is zero.
s = 0 + ½ x 9.8 x 42
s = height of balcony = 78.4m

Q.2. Jack dropped a stone from a cliff on Mars where the acceleration due to gravity is 3.3 m/s/s. The stone took 7seconds to hit the ground. How high was the cliff?

s = ut + ½ at2
If the stone is dropped rather than thrown down, the initial velocity is zero.
s = 0 + ½ x 3.3 x 72
s = height of cliff = 80.85m

Q.3. Nathan dropped a water bomb from a stationary hot-air balloon that was 49m above Leah's head. How long did the water bomb take to fall from the balloon and burst on Leah's head?

s = ut + ½ at2
If the water bomb is dropped rather than thrown down, the initial velocity is zero.
49= 0 + ½ x 9.8 x t2
49 = 4.9t2
t2 = 49/4.9 = 10
t = √10 = 3.16s

Q.4. Cate threw a stone vertically down from the roof of a tall building with an initial speed of 7m/s and it took 6 seconds to hit the ground below. How tall was the building?

s = ut + ½ at2
s = 7 x 6 + ½ x 9.8 x 62
s = 42 + 176.4 = 218.4m
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Q5. Adam threw a stone vertically upwards. The stone slowed as it went up and stopped momentarily, then gradually increased speed as it fell until it hit the ground 3 seconds after throwing. What was the maximum height reached by the stone?

The time for the stone to go up is equal to the time for the stone to fall down.
s = ut + ½ at2
Time to fall from maximum height = 1.5 seconds
s = 0 + ½ x 9.8 x 1.52
s = 11.025 = 11.03m (2 d.p.)

Q.6. Lisa threw a stone vertically down from a cliff on the Moon at 17m/s where the acceleration due to gravity is 1.7m/s/s. The stone hit the ground at the bottom of the cliff 5 seconds later. How high was the cliff?

s = ut + ½ at2
s = 17 x 5 + ½ x 1.7 x 172
s = 85 + 245.65 = 330.65m

Q7. Antonia threw a ball vertically down from a balcony of a very tall building. The ball hit the ground 1192.5 m below 15 seconds later. What was the speed with which the ball was thrown?

s = ut + ½ at2
1192.5 = u x 15 + ½ x 9.8 x 152
1192.5 = u x 15 + 110.25
15u = 1192.5 - 110.25 = 1082.25
u = 1082.25/15 = 72.15m/s

Q8. Samantha was in the basket of a hot-air balloon that was travelling upwards with a constant speed of 17 m/s. She held a water-bomb over the side of the basket and when the basket was a distance d above Chris's head she released the water bomb. The water-bomb hit Chris on the head 13 seconds later.
How far above Chris's head was the water bomb when it was released?

s = ut + ½ at2
Take down as positive
d = - 17 x 13 + ½ x 9.8 x 132
d = -221 + 828.1 = 607.1m

Q9. Pat had a hole in his pocket and a coin slipped out. How long would it take the coin to hit the floor 81 cm below?

s = ut + ½ at2
0.81 = 0 + ½ x 9.8 x t2
t2
= 0.81/4.9 = 0.1653
t = √(0.1653) = 0.4065 = 0.41s (2 d.p.)

Q10. A scientist on the newly discovered planet Eidum fired a projectile vertically upwards The projectile reached its maximum height of 354m 20 seconds later. What is the value of g, the acceleration due to gravity, on Eidum?
The time to rise to maximum height is equal to the time to fall from maximum height,
s = ut + ½ at2
354 = 0 + ½ g x 202
354 = 200g
g = 354/200 = 1.77m/s/s

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