a bullet is fire in a horizontal direction with a muzzle velocity of 300m/s in the absence of air resistance, how far will it have dropped in travely a horizontal distance of(a)20m?(b)40m?(c)60m? how far will it drop in one second
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To find the distance a bullet will have dropped in traveling a horizontal distance, we need to consider the time it takes for the bullet to cover that horizontal distance and the effect of gravity on its vertical motion.
Let's start by understanding the horizontal motion. Since the bullet is fired horizontally with a muzzle velocity of 300 m/s and there is no air resistance, the bullet will continue to move horizontally at a constant velocity throughout its motion.
(a) Distance dropped in traveling 20m:
Since the horizontal distance traveled is 20m, the time taken to cover this distance can be calculated using the equation: distance = velocity × time. Rearranging the equation, we have: time = distance / velocity.
So, time = 20m / 300m/s = 1/15 s.
Now, let's look at the vertical motion. Due to the effect of gravity, the bullet will undergo free fall in the vertical direction while moving horizontally.
The distance dropped in free fall can be determined using the formula: distance = 1/2 × acceleration × time^2.
In this case, the acceleration due to gravity is approximately 9.8 m/s^2. Plugging in the values, we get:
distance = 1/2 × 9.8 m/s^2 × (1/15 s)^2 = 0.0011 m (rounded to four decimal places).
Therefore, the bullet will have dropped approximately 0.0011 meters (or 1.1 millimeters) in traveling a horizontal distance of 20m.
(b) Distance dropped in traveling 40m:
Using the same formula distance = velocity × time, calculate the time:
time = 40m / 300m/s = 2/15 s.
Plugging in the values into the formula for the distance dropped in free fall:
distance = 1/2 × 9.8 m/s^2 × (2/15 s)^2 = 0.0088 m (rounded to four decimal places).
Therefore, the bullet will have dropped approximately 0.0088 meters (or 8.8 millimeters) in traveling a horizontal distance of 40m.
(c) Distance dropped in traveling 60m:
Again, calculate the time:
time = 60m / 300m/s = 1/5 s.
Using the same formula for the distance dropped in free fall:
distance = 1/2 × 9.8 m/s^2 × (1/5 s)^2 = 0.098 m (rounded to three decimal places).
Therefore, the bullet will have dropped approximately 0.098 meters (or 98 millimeters) in traveling a horizontal distance of 60m.
Now, let's consider how far the bullet will drop in one second:
To find the vertical distance dropped in one second independently of the horizontal distance traveled, we need to consider the effect of time rather than the horizontal distance.
Using the formula for the distance dropped in free fall, with time = 1s:
distance = 1/2 × 9.8 m/s^2 × (1s)^2 = 4.9 m.
Therefore, the bullet will have dropped approximately 4.9 meters in one second.