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Ms. Burns is at a window in a building and spots her worst enemy in a building across an 7.1m wide alley. If she throws a water balloon directly horizontally at a velocity of 6.35m/s, how far below her can her enemy be and still hit them?

User Charalamm
by
7.9k points

1 Answer

3 votes

Answer:

6.132 meters

Step-by-step explanation:

To solve this problem, we can use the following steps:

1. Identify the known and unknown quantities.

Known quantities:

  • Horizontal velocity of the water balloon, u = 6.35 m/s
  • Width of the alley, w = 7.1 m

Unknown quantity:

  • Maximum distance the water balloon can fall, h

2. Choose the appropriate equation of motion.

Since the water balloon is moving horizontally in free fall, we can use the following equation of motion:


\boxed{\boxed{\sf h = (1)/(2)\cdot g \cdot t^2} }

where:

  • h is the distance fallen
  • g is the acceleration due to gravity (9.81 m/s^2)
  • t is the time taken to fall

3. Solve for the unknown quantity.

We can rearrange the equation to solve for h:


\sf h = (1)/(2)\cdot g \cdot t^2

To find t, we can use the following equation of motion for horizontal motion:


\sf w = ut

where:

  • w is the distance traveled
  • u is the initial velocity
  • t is the time taken to travel the distance

Substituting in the known values, we get:


\sf 7.1 m = 6.35 m/s \cdot t

Solving for t, we get:


\sf t =(7.1)/(6.35)


\sf t = 1.1181102362204 s

Substituting this value back into the equation for h, we get:


\sf h = (1)/(2)\cdot 9.81 \cdot (1.1181102362204)^2


\sf h = 6.1320863041718137650195300648 m


\sf h = 6.132\textsf{ m in 3 d.p)}

Therefore, Ms. Burns' enemy can be up to 6.132 meters below her and she will still hit them with the water balloon.

User Chema
by
8.4k points
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