Question

A stone thrown horizontally from a height of 5.72 m hits the ground at a distance of 13.30 m. Calculate the initial speed of the stone. Neglect air resistance.

Answer 1

The initial horizontal speed of the stone thrown from a height of 5.72 m, hitting the ground at a distance of 13.30 m, was approximately 12.31 m/s.

Step-by-step explanation:

To calculate the initial speed of the stone, we will use the equations of motion for projectile motion, considering that the motion can be separated into two components: horizontal and vertical. Since air resistance is negligible, the horizontal velocity (νx) remains constant throughout the motion, and we can use the vertical motion to find the time.

We can use the following equation for the vertical motion, where h is the height (5.72 m) and g is the acceleration due to gravity (approximately 9.81 m/s²):

h = ½ g t²

Rearranging the equation to solve for the time (δ):

t = √(2h/g)

Substitute the given values:

t = √(2 * 5.72 m / 9.81 m/s²)

t = √(1.1644 s²)

t ≈ 1.08 s (time it takes for the stone to hit the ground)

Now we can find the initial horizontal speed using the horizontal motion equation where x is the horizontal distance (13.30 m):

x = νx t

Therefore, the initial speed is:

νx = x/t

νx = 13.30 m / 1.08 s

νx = 12.31 m/s

The initial speed of the stone was approximately 12.31 m/s horizontally.

Answer 2

initial velocity=12.31 m/s

Final speed= 16.234 m/s

Step-by-step explanation:

Given Data

height=5.72 m

distance=13.30 m

To Find

Initial Speed=?

Solution

Use the following equation to determine the time of the stone is falling.

d = vi ×t ½ ×9.8 × t²

Where

d = 5.72m and vi = 0 m/s

so

5.72 = ½× 9.8 ×t²

t = √(5.72 ÷ 4.9)

t=1.08 seconds

To determine the initial horizontal velocity use the following equation.

d = v×t

13.30 = v ×1.08

v = 13.30 ÷ 1.08

v=12.31 m/s

To determine stone’s final vertical velocity use the following equation

vf = vi+9.8×t............vi=0 m/s

vf = 9.8×1.08

vf= 10.584 m/s

To determine stone’s final speed use the following equation

Final speed = √[Horizontal velocity²+Final vertical velocity²]

Final speed = √{(12.31 m/s)²+(10.584 m/s)²}

Final speed= 16.234 m/s