Projectile Motion:- Equation 1: v = u + at

Q.1. Zac dropped a stone from a balcony. How fast was the stone travelling 2 seconds later?

Q.2. Luke dropped a spanner from the road level of the Watchamacallit Bridge. It was travelling at 41 m/s as it hit the water.
How long did it take to fall from the bridge to the water?

Q.3. Sabrina threw a stone vertically down from the top of a cliff with an initial speed of 14 m/s.
How fast was it going as it hit the ground 3 seconds later?

Q.4. Ly threw a ball vertically down from a balcony and it hit the ground 2 seconds later at 41 m/s.
What was the speed with which Ly threw the ball down?

Q.5. Alain threw a stone vertically up from a cliff top at 13 m/s. The stone slowed as it went up and stopped momentarily, then gradually increased speed until it hit the ground at the bottom of the cliff 4 seconds later.
How fast was the stone travelling as it hit the ground?

Q6. Antonia threw a ball vertically down from a balcony. The ball reached a speed of 23 m/s in 2seconds.
What was the speed with which the ball was thrown?

Q7. Nathan threw a water balloon vertically down from a balcony with an initial velocity of 21 m/s vertically down. How fast was the balloon travelling when it hit Leah on the head 3 seconds later?

Q8. Pat dropped a coin from a balcony. How long would it take the coin to reach a speed of 60 m/s?

Q9. Ben dropped a spanner from the Moon lander and it hit the surface of the Moon 4 seconds later. 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 263 m/s. The rocket reached its maximum height 25 seconds later.
What is the value of g, the acceleration due to gravity, on Seitsew?


Answers:

Q.1. Zac dropped a stone from a balcony. How fast was the stone travelling 2 seconds later?

v = u + at
Initial velocity = zero m/s down
v = 0 + 9.8 x 2 = 19.6 m/s

Q.2. Luke dropped a spanner from the road level of the Watchamacallit Bridge. It was travelling at 41 m/s as it hit the water.
How long did it take to fall from the bridge to the water?

v = u + at
41 = 0 + 9.8 x t
t = 41/9.8 = 4.18367 = 4.2 s (2 d.p.)

Q.3. Sabrina threw a stone vertically down from the top of a cliff with an initial speed of 14 m/s.
How fast was it going as it hit the ground 3 seconds later?

v = u + at
v = 14 + 9.8 x 3
v = 43.4 m/s

Q.4. Ly threw a ball vertically down from a balcony and it hit the ground 2 seconds later at 41 m/s.
What was the speed with which Ly threw the ball down?

v = u + at
41 = u + 9.8 x 2
41 = u + 19.6
u = 41 - 19.6 = 21.4 m/s

Q.5. Alain threw a stone vertically up from level ground at 13 m/s. The stone slowed as it went up and stopped momentarily, then gradually increased speed until it hit the ground 4 seconds later.
How fast was the stone travelling as it hit the ground?

On level ground time to go up = time to come down so the stone took 2 seconds to reach maximum height and a further 2 seconds to fall back to the ground from maximum height.
Also the initial speed going up is equal to the final speed coming down
So the stone hit the ground at 13 m/s

Q6. Antonia threw a ball vertically down from a balcony. The ball reached a speed of 23 m/s in 2seconds.
What was the speed with which the ball was thrown?

v = u + at
23 = u + 9.8 x 2 = u + 19.6
u = 23 - 19.6 = 3.4 m/s

Q7. Nathan threw a water balloon vertically down from a balcony with an initial velocity of 21 m/s vertically down. How fast was the balloon travelling when it hit Leah on the head 3 seconds later?

v = u + at
v = 21 + 9.8 x 3 = 21 + 29.4 = 50.4 m/s

Q8. Pat dropped a coin from a balcony. How long would it take the coin to reach a speed of 60 m/s?

v = u + at
60 = 0 + 9.8 t
t = 60/9.8 = 6.12245 s = 6.1s (1 d.p)

Q9. Ben dropped a spanner from the Moon lander and it hit the surface of the Moon 4 seconds later. 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?

v = u + at
v = 0 + 1.6 x 4 = 6.4 m/s

Q10. A scientist on the newly discovered planet Seitsew fired a rocket vertically upwards with a velocity of 263 m/s. The rocket reached its maximum height 25 seconds later.
What is the value of g, the acceleration due to gravity, on Seitsew?

v = u + at
Define either up or down as positive (it is up to you) and pay particular attention to the sign of all quantities.
Method 1: Define up as positive.
v = 0 (velocity at maximum height is zero)
u = + 263 m/s (up is positive and initial velocity is up)
t 25 s. It is a scalar and has no direction
g = a = ?
v = u + at
0 = 263 + a x 25
0 = 263 + 25t
t = -263/25 = - 10.52 m/s/s
Note that we defined up as positive and gravity acts down so it is negative

Method 2: Define down as positive.
v = 0 (velocity at maximum height is zero)
u = -263 m/s (up is negative and initial velocity is up)
t 25 s. It is a scalar and has no direction
g = a = ?
v = u + at
0 = -263 + a x 25
0 = -263 + 25t
t = 263/25 = 10.52 m/s/s
Note that we defined down as positive and gravity acts down so it is positive

When giving direction for gravity always give the direction as down. This removes any confusion about + or - signs.
a = g = - 9.8 m/s/s (gravity acts downwards and we have defined up as positive hence a is negative)