A Rifle Is Aimed Horizontally At A Target 30m Away. The Bullet Hits The Target 1.9cm Below The Aiming Point. (A) What Is The Bullet's Time Of Flight? (B) What Is The Muzzle Velocity?
time to fall 1.9cm:
h=1/2 g t^2, or t= sqrt(2h/g)=sqrt(.028/9.8) sec = .0534sec
speed= distance/time=30m/.0534=562m/s
I can not solve this problem
To solve this problem, we can use the equations of motion for a projectile. Let's assume that the bullet was fired with an initial velocity v₀ and the acceleration due to gravity is g = 9.8 m/s².
(A) To determine the time of flight, we can use the vertical motion equation:
Δy = v₀y * t + (1/2) * g * t²
Since the bullet was fired horizontally, its initial vertical velocity v₀y is 0. The change in height Δy is given as 1.9 cm, which is equal to 0.019 m. Substituting these values into the equation, we get:
0.019 m = 0 * t + (1/2) * 9.8 m/s² * t²
Simplifying the equation, we get:
4.9t² = 0.019
Dividing both sides by 4.9, we get:
t² = 0.019 / 4.9
t² = 0.003877551
Taking the square root of both sides, we find:
t = √(0.003877551)
t ≈ 0.0623 s
So, the bullet's time of flight is approximately 0.0623 seconds.
(B) To determine the muzzle velocity, we can use the horizontal motion equation:
Δx = v₀x * t
The horizontal distance Δx is given as 30 m, and the time of flight t is 0.0623 s. Therefore, the equation becomes:
30 m = v₀x * 0.0623 s
Dividing both sides by 0.0623 s, we get:
v₀x ≈ 481.45 m/s
So, the muzzle velocity of the bullet is approximately 481.45 m/s.
To solve this problem, we will use the equations of motion for projectile motion. Let's break it down step by step:
(A) To find the bullet's time of flight, we need to determine how long it takes for the bullet to travel 30m horizontally. We can use the equation for horizontal motion:
Distance = Velocity x Time
Since the bullet's motion is horizontal, there is no vertical acceleration acting on it, and hence, no vertical displacement. Therefore, the vertical motion does not affect the time of flight.
Now, we have the information that the bullet hits the target 1.9cm below the aiming point. This vertical displacement will be useful to find the bullet's time of flight. Since the bullet is falling downward due to gravity, we can use the equation for vertical displacement:
-1/2 x g x (Time^2) = -0.019m
Here, 'g' represents the acceleration due to gravity (approximately 9.8 m/s^2), and 'Time' is the time of flight we need to find.
By substituting the given values, the equation becomes:
-4.9 x (Time^2) = -0.019
By rearranging the equation and solving for 'Time', we get:
(Time^2) = 0.019 / 4.9
Time = √(0.019 / 4.9)
Calculating this, we find that Time ≈ 0.097 seconds.
So, the bullet's time of flight is approximately 0.097 seconds.
(B) To determine the muzzle velocity of the bullet, we can use the equation for horizontal velocity:
Velocity = Distance / Time
Substituting the known values, we have:
Velocity = 30m / 0.097s
Velocity ≈ 309.28 m/s
Therefore, the muzzle velocity of the bullet is approximately 309.28 m/s.