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A shopping cart with two nice kids, rolls off a horizontal roof ledge that is 50
meters high. The cart and nice kids land 30 meters from the base of the ledge.
How fast was the cart rolling when it left the ledge?

Sagot :

Supernova

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.

luvadri

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.

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