Solve the problem. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the objects
-A projectile is fired at a speed of 800 m/sec at an angle of 34°. How long will it take to get 20 km downrange? Round your answer to the nearest whole number.
A) 32 sec
B) It will never get that far downrange.
C) 30 sec
D) 28 sec

Question

Quizplus · Accepted Answer

To find the time it takes for the projectile to travel 20 km (or 20,000 meters) downrange, we use the formula for horizontal distance in projectile motion: $d = v \cos(\theta) t$, where $d$ is the distance, $v$ is the initial velocity, $\theta$ is the launch angle, and $t$ is the time. Rearranging for $t$, we get $t = \frac{d}{v \cos(\theta)}$. Plugging in the given values ($d = 20000$ m, $v = 800$ m/s, $\theta = 34^\circ$), we find $t = \frac{20000}{800 \cos(34^\circ)}$. Calculating this gives $t \approx 30$ seconds.

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