A person holds a rifle horizontally and fires at a target. The bullet has a muzzle...

A person holds a rifle horizontally and fires at a target. The bullet has a muzzle speed of 200m/s and the person hears the bullet strike the target 1.00s after firing it. The air temp is 72 degrees Fahrenheit. What is the distance to the target?

Solutions

Expert Solution

The temperature is for the speed of sound in this case which is 340 m/sec at 72 F (searched from google). Actually the total time (1 sec) is the time required by the bullet to reach the target (strike the target and make a sound) plus the time required by the sound to reach back to the person.

Speed of bullet = vb = 200 m/sec
Speed of sound = vs = 340 m/sec
Distance travelled by both = S = ? (it is same for both)
time taken by bullet = tb
time taken by sound = ts

By the conditions of the question:
tb + ts = 1 => tb = 1 - ts
and
tb x vb = ts x vs = S
putting values
(1 - ts) x 200 = ts x 340
200 - 200ts = 340ts
200 = 340ts + 200ts
200 = 540ts
ts = 200/540 = 0.37037 sec
tb = 1 - 0.37037 = 0.62963 sec

S = vb x tb = 200 x 0.62963 = 125.93 m
S = vs x ts = 340 x 0.37037 = 125.93 m

Therefore, the distance between the target and the person is 125.93 meters.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A person holds a rifle horizontally and fires at a target. The bullet has a muzzle...

A person holds a rifle horizontally and fires at a target. The bullet has a muzzle speed of 155 m/s, and the person hears the bullet strike the target 0.70 s after firing it. The air temperature is 77°F. What is the distance to the target

A rifle with a weight of 25 N fires a 5.5 g bullet with a speed...

A rifle with a weight of 25 N fires a 5.5 g bullet with a speed of 210 m/s. (a) Find the recoil speed of the rifle. m/s (b) If a 675 N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle. m/s

A bullet is fired horizontally at a stationary 7.0 kg target. The target sits on a...

A bullet is fired horizontally at a stationary 7.0 kg target. The target sits on a frictionless horizontal surface and is connected to a spring on the backside of the target. The spring has a spring constant of 5000 N/m. The 11.0 g bullet is traveling horizontally at 675 m/s the moment before it strikes the target. After 1 ms, the bullet is embedded into the target and begins to oscillate. Ignore air resistance. (a) Determine the speed of the...

A rifle is aimed horizontally at the center of a large target 50.4 m away. If...

A rifle is aimed horizontally at the center of a large target 50.4 m away. If the distance from the center of the target to the point where the bullet strikes the target is 1.51 cm, calculate the initial speed of the bullet in m/s?

A rail-gun fires a tungsten projectile horizontally with an exit muzzle velocity of 1500 m/s. The...

A rail-gun fires a tungsten projectile horizontally with an exit muzzle velocity of 1500 m/s. The horizontal acceleration of the projectile is given as ax = -40vx^2 + 125000vx - 96900000 where vx = horizontal velocity. The muzzle is 50 meters off the ground. At what distance, in meters, from the muzzle will the projectile strike the ground if the ground remains level? Do not neglect the effects due to gravity. Please help, I don't understand how to do this...

A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod...

A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.10 m and mass 8.56 kg , find the torque the person must exert on the ladder to give it an angular acceleration of 0.238 rad/s2 .

Agent Arlene devised the following method of measuring the muzzle velocity of a rifle (the figure...

Agent Arlene devised the following method of measuring the muzzle velocity of a rifle (the figure below). She fires a bullet into a 4.114-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 164.2 N/m . The bullet, whose mass is 7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be 9.460 cm . What is the speed v of the...

A rifle of mass M is initially at rest. A bullet of mass m is fired...

A rifle of mass M is initially at rest. A bullet of mass m is fired from the rifle with a velocity v relative to the ground. Which one of the following expressions gives the velocity of the rifle relative to the ground after the bullet is fired? A) −mv B) mv C) Mv/m D) mv/M

Show a complete derivation of the “muzzle speed” of the bullet from the ballistic pendulum. You...

Show a complete derivation of the “muzzle speed” of the bullet from the ballistic pendulum. You will use conservation of energy and conservation of momentum to determine vmuzzle in terms of mB the mass of the bullet, MP the mass of the pendulum, and h the change in height of the combined pendulum/bullet mass after they stick together. This will be called the “ballistic pendulum equation”

A large crate is suspended by a light string. A bullet is fired horizontally into the...

A large crate is suspended by a light string. A bullet is fired horizontally into the crate and becomes firmly lodged inside it. After being struck by the bullet, the crate swings upward to a maximm height and then swings back up. Just before the collision (time t1), the crate is at rest and the bullet moves horizontally with speed v0. Immediately after the bullet becomes lodged inside the crate (time t2) the bullet and crate move together with speed...

Subjects