Question

The shells fired from an artillery piece have a muzzle speed of 240m/s and the target is at a horizontal distance of 1.40km two possible angles can be used to hit the target. find the smaller angle relative to the horizontal at which the gun should be aimed?

Answer 1

To find the smaller angle at which the gun should be aimed to hit the target, we can use the concept of projectile motion. We first find the time of flight using the equation t = distance / horizontal velocity. Then, we find the vertical velocity using the equation Vv = gt, where g is the acceleration due to gravity. Finally, we find the angle using the equation θ = arctan(Vv / horizontal velocity). The smaller angle is 86.70°.

Step-by-step explanation:

To find the smaller angle at which the gun should be aimed to hit the target, we can use the concept of projectile motion. In this case, the target is at a horizontal distance of 1.40 km from the gun and the muzzle speed of the shells is 240 m/s.

We can use the equation for horizontal range to find the time of flight and then use the equation for vertical motion to find the angle relative to the horizontal.

1. First, let's find the time of flight (t) using the equation: t = distance / horizontal velocity. Therefore, t = 1.40 km / (240 m/s) = 5833.33 s.
2. Next, let's find the vertical velocity (Vv) using the equation: Vv = gt, where g is the acceleration due to gravity (9.8 m/s^2). Therefore, Vv = (9.8 m/s^2) * (5833.33 s) = 57083.33 m/s.
3. Now, let's find the angle (θ) using the equation: θ = arctan(Vv / horizontal velocity). Therefore, θ = arctan(57083.33 m/s / 240 m/s) = 86.70°.

Therefore, the smaller angle relative to the horizontal at which the gun should be aimed is 86.70°.

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