How far bullet travels in 2,5 seconds

[whatdoido]

I am solving some problems of my physics book for fun and for some reason I am getting a wrong answer from this one.

1. Homework Statement

A bullet is shot at an angle of 35^o with a speed of 90 m/s. I assume that air resistance is ignored.

Calculate bullet's distance from launch site 2,5 seconds after the shot.

Homework Equations

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x = v_ox * t
v_ox = v_o * cosθ

The Attempt at a Solution

[/B]
The horizontal speed should stay as it is.

v_o = 90 m/s
t = 2,5 s
θ = 35^o

x = v_ox * t = v_o * cosθ * t = 90 m/s * cos 35^o * 2,5 s = 184,309... m ≈ 184 m

The book says that the answer should be 210 m. I cannot think of any other way to solve this.

 

[Fightfish]

The question asked for distance from the launch site, not just the horizontal distance. After 2.5 seconds, the bullet is still in the air, so the vertical distance is nonzero.

 

[gneill]

Has the bullet landed by time t = 2.5 s? If not, what are its coordinates with respect to the launch point?

 

[whatdoido]

The question asked for distance from the launch site, not just the horizontal distance. After 2.5 seconds, the bullet is still in the air, so the vertical distance is nonzero.

Okay, thanks this helped!

I calculated the vertical distance, y:

y = v_oy * t - 0,5 * g * t²
= v_o * sinθ * t - 0,5 * g * t²
= 90 m/s * sin 35^o * 2,5 s - 0,5 * 9,81 m/s² * (2,5 s)²
= 98,398...m

Then I figured that the real distance, d, is the hypotenuse of x and y.

d = √(x² + y²) = √((184,309... m)² + (98,398... m)²)
= 208,930... m
≈ 210 m

This should be correct way to do it, right?

 

[PeroK]

Right!