Question

A shopping cart with two nice kids, rolls off a horizontal roof ledge that is 50

Answer 1

Answer:

9.39 m/s

Explanation:

Using the y-direction, we can solve for the time t it takes for the cart to reach the ground.

Assume the up direction is positive and the down direction is negative.

• v₀ = 0 m/s
• a = -9.8 m/s²
• Δy = -50 m
• t = ?

Find the constant acceleration equation that contains these four variables.

• Δy = v₀t + 1/2at²  

Substitute known values into this equation.

• -50 = (0)t + 1/2(-9.8)t²

Multiply and simplify.

• -50 = -4.9t²

Divide both sides of the equation by -4.9.

• 10.20408163 = t²

Square root both sides of the equation.

• t = 3.194382825

Now we can use this time t and solve for v₀ in the x-direction. Time is most often our link between vertical and horizontal components of projectile motion.  

List out known variables in the x-direction.

• v₀ = ?
• t = 3.194382825 s
• a = 0 m/s²
• Δx = 30 m

Find the constant acceleration equation that contains these four variables.

• Δx = v₀t + 1/2at²  

Substitute known values into the equation.

• 30 = (v₀ · 3.194382825) + 1/2(0)(3.194382825)²

Multiply and simplify.

• 30 = v₀ · 3.194382825

Divide both sides of the equation by 3.194382825.

• v₀ = 9.391485505

The cart was rolling at a velocity of 9.39 m/s (initial velocity) when it left the ledge.

Answer 2

Answer:

9.39 m/s

Explanation:

Using the y-direction, we can solve for the time t it takes for the cart to reach the ground.

Assume the up direction is positive and the down direction is negative.

v₀ = 0 m/s

a = -9.8 m/s²

Δy = -50 m

t = ?

Find the constant acceleration equation that contains these four variables.

Δy = v₀t + 1/2at²  

Substitute known values into this equation.

-50 = (0)t + 1/2(-9.8)t²

Multiply and simplify.

-50 = -4.9t²

Divide both sides of the equation by -4.9.

10.20408163 = t²

Square root both sides of the equation.

t = 3.194382825

Now we can use this time t and solve for v₀ in the x-direction. Time is most often our link between vertical and horizontal components of projectile motion.  

List out known variables in the x-direction.

v₀ = ?

t = 3.194382825 s

a = 0 m/s²

Δx = 30 m

Find the constant acceleration equation that contains these four variables.

Δx = v₀t + 1/2at²  

Substitute known values into the equation.

30 = (v₀ · 3.194382825) + 1/2(0)(3.194382825)²

Multiply and simplify.

30 = v₀ · 3.194382825

Divide both sides of the equation by 3.194382825.

v₀ = 9.391485505

The cart was rolling at a velocity of 9.39 m/s (initial velocity) when it left the ledge.