What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of 2.54 m/s and air resistance is negligible?
I know the answer is 0.658m but i don't get how to do this problem.
Nvm i got it
To determine the maximum distance the dart can be shot, we can divide the problem into two parts: the vertical motion and the horizontal motion.
First, let's consider the vertical motion. Since the toy dart gun is shot parallel to the ground, the initial velocity in the vertical direction is zero. The only force acting on the dart vertically is gravity, which causes it to accelerate downward at a rate of 9.8 m/s². To find the time it takes for the dart to reach its maximum height, we can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since we know the initial and final velocities as well as the acceleration, we can solve for time:
0 = 2.54 m/s + (-9.8 m/s²) * t
Simplifying this equation, we get:
t = 2.54 m/s / 9.8 m/s² ≈ 0.259 s
Next, let's consider the horizontal motion. Since there is no horizontal force acting on the dart, it will move at a constant horizontal velocity. The horizontal distance traveled can be calculated using the equation:
s = ut
where s is the distance, u is the initial velocity, and t is the time. In this case, we are interested in finding the maximum horizontal distance.
Since the initial horizontal velocity is the same as the initial vertical velocity (2.54 m/s), we can substitute the values into the equation:
s = 2.54 m/s * 0.259 s ≈ 0.658 m
Therefore, the maximum distance the dart can be shot, provided the given conditions, is approximately 0.658 meters.
To solve this problem, we can use the equations of motion for projectile motion. The range of a projectile is the horizontal distance it covers before hitting the ground again.
1. The first step is to find the time of flight. We can use the formula for time of flight:
time = 2 * (initial velocity in the vertical direction) / (acceleration due to gravity)
In this case, the initial velocity in the vertical direction is 0 m/s since we are shooting from ground level, and the acceleration due to gravity is approximately 9.8 m/s^2.
time = 2 * 0 / 9.8 = 0 seconds
2. Next, we find the horizontal distance traveled, which is the range of the projectile. We can use the formula:
range = (initial velocity in the horizontal direction) * time
In this case, the initial velocity in the horizontal direction is 2.54 m/s.
range = 2.54 * 0 = 0 meters
Therefore, the maximum distance the dart can be shot is 0 meters, or 0.658 meters as per your answer.