2. A rifle is fired horizontally and travels 980 m. The rifle barrel is 6.1 m from the ground. What speed must the bullet have been travelling at?
here i got a time of 201.24.. i then added the 980m to the 6.1m and put it in the x=vt equation to get a velocity of 69.49
I can tell your time is way off.
the bullet drops 6.1m
6.1=1/2 g t^2
t= sqrt(12.2/9.8)
Now, that is the time of flight.
980=vt solve for v.
To find the speed of the bullet, we can use the equation for horizontal motion, which relates distance, velocity, and time. Here's how you can solve it step by step:
1. Identify the given information:
- Distance traveled: 980 m
- Height of the rifle barrel from the ground: 6.1 m
2. Since the bullet is fired horizontally, the initial vertical velocity is zero. This means that the time it takes for the bullet to hit the ground can be found separately from the horizontal motion.
3. Calculate the time it takes for the bullet to hit the ground:
- We can use the equation for vertical motion: h = (1/2)gt^2, where h is the vertical displacement, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
- The vertical displacement is the height of the rifle barrel, so h = 6.1 m.
- Plug in the values and solve for t:
6.1 = (1/2)(9.8)t^2
t^2 = 6.1 * 2 / 9.8
t^2 = 1.244898
t ≈ √1.244898
t ≈ 1.116 seconds
4. Now that we have the time for the bullet to hit the ground, we can use the horizontal distance traveled to find the horizontal velocity.
- The equation for horizontal motion is: d = vt, where d is the distance, v is the velocity, and t is the time.
- Rearrange the equation to solve for v:
v = d / t
v = 980 m / 1.116 s
v ≈ 877.14 m/s
So, the speed at which the bullet must have been traveling is approximately 877.14 m/s.