For this problem, ignore air resistance.
You are to fire a rifle that shoots a particular bullet at 460 m/s at a target that is 45.7 m away and level with the rifle. Assuming that the acceleration due to gravity is 9.80 m/s², how high above the target must the barrel of the rifle be aimed such that the bullet hits the target?
* Physics - bobpursley, Wednesday, October 6, 2010 at 4:14pm
The real question is how far the bullet falls vertically during the trip.
timeinair=45.7m/460m/s
how far does an object fall in that time?
h=1/2 g t^2
* Physics - Steven, Wednesday, October 6, 2010 at 4:57pm
That's not entirely correct... That would only be true if the rifle was fired horizontally, giving the x component 460 m/s towards the target.
However, that 460 m/s has some UPWARD y component too, reducing the x component by some amount...
Thanks,
Steven
* Physics - Damon, Wednesday, October 6, 2010 at 5:06pm
Forget that upward component. Too fast to be significant. look at 460 cos (angle up)
the cosine of your angle up will be essentially 1 and the sine will be about 0
* Physics - Steven, Wednesday, October 6, 2010 at 8:37pm
I would like to forget the upward component, as the object IS in fact a bullet fired at a fast velocity from a gun towards a target not too far away.
However, we're graded on the correctness of our problem solving. And, additionally, this factor WOULD become an issue if we were firing a marshmallow gun or a pea shooter at this distance, or if you were firing a sniper rifle at a target over a mile away.
Thanks,
Steven
To solve this problem, we need to find out how high above the target the barrel of the rifle must be aimed.
First, let's calculate the time it takes for the bullet to reach the target horizontally. We can use the formula:
timeinair = distance / horizontal velocity
Given:
distance = 45.7 m
horizontal velocity = 460 m/s
timeinair = 45.7 m / 460 m/s
timeinair = 0.0993 s (rounded to 4 decimal places)
Next, we need to find out how far the bullet falls vertically during this time. Since the bullet is fired horizontally, it will not have any initial vertical velocity.
Using the formula for vertical displacement due to gravity:
vertical displacement = 0.5 * acceleration due to gravity * time^2
Given:
acceleration due to gravity = 9.8 m/s^2
time = 0.0993 s
vertical displacement = 0.5 * 9.8 m/s^2 * (0.0993 s)^2
vertical displacement = 0.0483 m (rounded to 4 decimal places)
Therefore, the barrel of the rifle must be aimed approximately 0.0483 meters (or 4.83 cm) above the target.
To solve this problem, we need to calculate how high above the target the rifle barrel must be aimed in order for the bullet to hit the target. We can ignore air resistance for this problem.
First, let's consider the horizontal motion of the bullet. The bullet is shot with a velocity of 460 m/s and the target is 45.7 m away. We can use the equation s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
Since the target is at the same level as the rifle, there is no vertical displacement, so the equation becomes s = ut.
Plugging in the values, we have s = 460 m/s * t and s = 45.7 m.
Now, let's consider the vertical motion of the bullet. We know that the acceleration due to gravity is -9.80 m/s^2 (negative because it acts downwards). We want to find the height above the target, so we'll call it h.
Using the equation h = (1/2)gt^2, we can substitute the time from the horizontal motion equation.
h = (1/2) * (-9.80 m/s^2) * t^2
We know that t = s / u, so we can substitute this into the equation.
h = (1/2) * (-9.80 m/s^2) * (s / u)^2
Simplifying further, we have
h = (1/2) * (-9.80 m/s^2) * (45.7 m / 460 m/s)^2
Calculating this expression, we find that h is approximately -0.457 m (negative because the height is below the target).
Therefore, in order for the bullet to hit the target, the barrel of the rifle must be aimed 0.457 m below the target.