Question

PLZ HELP ME

1. A stone is thrown horizontally from a cliff 30m high with an initial speed of 20m/s. How far from the cliff does the stone strike the ground?


2. A ball rolls off the edge of a table 1.44m above the floor and strikes the floor at a point 2m horizontally from the edge of the table.

A) What is the time the ball was in the air?


B) What is the initial velocity of the ball?



3. A golfer hits a ball and gives it an initial velocity of 40 m/s, at an angle of 30º above the horizontal.

A) How long does the ball stay in the air?


B) How far horizontally (the range) does the ball travel before hitting the ground?

Answer 1

1. The stone will strike the ground 49.46 m from the base of the cliff

2. A) Approximately 0.542 seconds

B) Approximately 3.69 m/s

3. A) The time the ball spends in the air is approximately 4.0775 s

B) The horizontal range is approximately 141.25 m.

Step-by-step explanation:

1. The time it takes the stone to land is given by the equation, t = √(h/(1/2 × g)

∴ t = √(30/(1/2 × 9.81)) ≈ 2.473 seconds

The horizontal distance covered by the stone in that time = 20 × 2.473 ≈ 49.46 m

The stone will strike the ground 49.46 m from the base of the cliff

2. A) The time the ball spends in the air = t = √(h/(1/2 × g)

∴ t = √(1.44/(1/2 × 9.81)) ≈ 0.542 seconds

B) The initial horizontal velocity, u = Horizontal distance/(Time) = 2/0.542 ≈ 3.69 m/s

The initial horizontal velocity ≈ 3.69 m/s

3. A) The time the ball spends in the air is given by the following equation;

t = 2 × u × sin(θ)/g = 2 × 40 × sin(30)/9.81 ≈ 4.0775 s

t ≈ 4.0775 s

B) The horizontal range, R, of the ball is given by the equation for the range of a projectile as follows;

`Range, R = (u^2 * sin (2 \cdot \theta) )/(g)`

Substituting the known values, gives;

`Range, R = (40^2 * sin (2 * 30^(\circ)) )/(9.81) \approx 141.25 \ m`

The horizontal range ≈ 141.25 m.