The speed of a bullet as it travels down the barrel of a rifle toward the openin

Question

The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by y = (-4.60 x 10^7) t^2 + (3.00 x 10^5) t, where v s n meters per second and t s in seconds. The acceleration of the bullet just as t leaves the barrel is zero. (a) Determine the acceleration and position of the bullet as a function of time when the bullet s n the barrel. (Use t as necessary and round all numerical coefficients to exactly 3 significant figures.) a = m/s^2 x= [ ] m (b) Determine the length of time the bullet is accelerated. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, s (c) Find the speed at which the bullet leaves the barrel. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s (d) What is the length of the barrel? Your response differs from the correct answer by more than 10%. Double check your calculations. m

Explanation / Answer

v = xt^2 + yt
where x = -4.6 * 10^7
y = 3.0 * 10^5

acceleration a = dv/dt
a = d/dt (xt^2 + yt)
a =2xt + y
a = - 2*4.6 * 10^7 t + 3.0 * 10^5 m/s^2
a = -9.2 * 10^7 t + 3.0 * 10^5 m/s^2


Position x = v.dt
x = (xt^2 + yt) dt
x = xt^3 / 3 + yt^2 /2
x = -4.6 * 10^7 /3 t^3 + 3.0 * 10^5 /2 t^2
x = -1.53 *10^7 t^3 + 1.5 * 10^5 t^2

b)
As the acceleration of the bullet = 0 when it leaves the barrel
-9.2 * 10^7 t + 3.0 * 10^5 m/s^2 = 0
t = 3.0 * 10^5 / 9.2 * 10^7
t = 0.00326 s
t = 3.26 ms

c)
v = -4.6 * 10^7 *t^2 + 3.0 * 10^5 *t
v = -4.6 * 10^7 *(0.00326)^2 + 3.0 * 10^5 *0.00326
v = 489.13 m/s^2
Speed at which bullet leaves the barrel v = 489.13 m/s^2

d)
s = -1.53 *10^7 t^3 + 1.5 * 10^5 t^2
s =  -1.53 *10^7 ( 0.00326 )^3 + 1.5 * 10^5 ( 0.00326 )^2
s = 1.064 m
Length of Barrel s = 1.064 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.