A sled and rider, gliding over horizontal, frictionless ice at 4.0 m/s, have a combined mass of 80 kg. The sled then slides over a rough spot in the ice, slowing down to 3.0 m/s. What impulse was delivered to the sled by the friction force from the rough spot?

An ice hockey puck slides along the ice at 12 m/s. A hockey stick delivers an impulse of $4.0 \mathrm { kg } \cdot \mathrm { m } / \mathrm { s }$, causing the puck to move off in the opposite direction with the same speed. What is the mass of the puck?

A child is sliding on a sled at 1.5 m/s to the right. You stop the sled by pushing on it for 0.50 s in a direction opposite to its motion. If the mass of the child and sled is 35 kg, what average force do you need to apply to stop the sled? Use the concepts of impulse and momentum.

Use the impulse-momentum theorem to find how long a stone falling straight down takes to increase its speed from 5.5 m/s to 10.4 m/s.

A 5000 kg train car, with its top open, is rolling on frictionless rails at 22.0 m/s. What mass of water has collected in the car?

A 20 g ball is fired horizontally with initial speed $v _ { \mathrm { i } }$ toward a 100 g ball that is hanging motionless from a 1.0-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 100 g ball swings out to a maximum angle $\theta _ { \max } = 50 ^ { \circ }$. What was $v _ { i }$?

A sled slides without friction down a small, ice-covered hill. On its first run down the hill, the sled starts from rest at the top of the hill and its speed at the bottom is $7.50 \mathrm{~m} / \mathrm{s}$. On a second run, the sled starts with a speed of $1.50 \mathrm{~m} / \mathrm{s}$ at the top. What is the speed of the sled at the bottom of the hill on the second run?

A sled slides without friction down a small, ice-covered hill. On its first run down the hill, the sled starts from rest at the top of the hill and its speed at the bottom is $7.50 \mathrm{~m} / \mathrm{s}$. On a second run, the sled starts with a speed of $1.50 \mathrm{~m} / \mathrm{s}$ at the top. What is the speed of the sled at the bottom of the hill on the second run?

Phil and his rocket-powered sled have a combined mass M and are accelerating at a rate a when the sled runs into Mala, mass m, who tumbles aboard. (a) Show that the sled now accelerates at a rate equal to $\frac{M}{M+m} a$. (b) If Phil and his sled have a combined mass of $70 {kg}$, Mala's mass is $45{kg}$, and the initial acceleration of the sled was $3.6 {m} / {s}^2$, show that when Mala joins Phil the acceleration of the sled is $2.2 {m} / {s}^2$.

A 9.5 kg dog takes a nap in a canoe and wakes up to find the canoe has drifted out onto the lake but now is stationary. He walks along the length of the canoe at 0.50 m/s, relative to the water, and the canoe simultaneously moves in the opposite direction at 0.15 m/s. What is the mass of the canoe?

A sled slides without friction down a small, ice-covered hill. If the sled starts from rest at the top of the hill, its speed at the bottom is $7.50 \mathrm{~m} / \mathrm{~s}$. On a second run, the sled starts with a speed of $1.50 \mathrm{~m} / \mathrm{~s}$ at the top. When it reaches the bottom of the hill, is its speed $9.00 \mathrm{~m} / \mathrm{~s}$, more than $9.00 \mathrm{~m} / \mathrm{~s}$, or less than $9.00 \mathrm{~m} / \mathrm{~s}$ ? Explain.

A sled slides without friction down a small, ice-covered hill. If the sled starts from rest at the top of the hill, its speed at the bottom is 7.50 m/s. (a) On a second run, the sled starts with a speed of 1.50 m/s at the top. When it reaches the bottom of the hill, is its speed 9.00 m/s, more than 9.00 m/s, or less than 9.00 m/s? Explain. (b) Find the speed of the sled at the bottom of the hill after the second run.

A sled slides without friction down a small, ice-covered hill. If the sled starts from rest at the top of the hill, its speed at the bottom is $7.50 \mathrm{~m} / \mathrm{~s}$. Determine the speed of the sled at the bottom of the hill after the second run.

A $57\text{ g}$ tennis ball is served at $45\,\dfrac{\text{m}}{\text{s}}$. If the ball started from rest, what impulse was applied to the ball by the racket?