# Imagine that a bullet is shot vertically into the air with an initial

**1. The problem statement, all variables and given/known data**

Imagine that a bullet is shot vertically into the air with an initial speed of 9800 m/s. If we ignore air friction, how high will it go?

v_{i} = 9800 m/s

h = ?

**2. Relevant equations**

v^{2} = v_{i}^{2} + 2aΔy

K_{i} = U_{i} –> 1/2mv^{2} = mgh

F = (Gm_{1}m_{2})/r

**3. The attempt at a solution**

Attempt 1

v^{2} = v_{i}^{2} + 2aΔy

0 = (9800 m/s)^{2} + 2(-9.8 m/s^{2})(Δy)

Δy = 4,900,000 m

Attempt 2

1/2mv^{2} = mgh

h = 4,900,000 m

Neither of these equations worked, so I tried using gravitational equations, but I couldn’t figure it out.

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