In pushing a 0.024-kg dart into a toy dart gun, you have to exert an increasing force that tops out at 6.0 N when the spring is compressed to a maximum value of 0.12 m. (a) What is the launch speed of the dart when fired horizontally? (b) Does your answer change if the dart is fired vertically?

(II) You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

Solve for the variable indicated. C=2πr for r

The spring constant of a toy dart gun is $5000 \mathrm{~N} / \mathrm{m}$. To cock the gun the spring is compressed $3 \mathrm{~cm}$. The 7-g dart, fired straight upward, reaches a maximum height of $24 \mathrm{~m}$. Determine the energy dissipated by air friction during the dart's ascent. Estimate the speed of the projectile when it returns to its starting point.

A spring gun (k=28 N/m) is used to shoot a 56 g ball horizontally. Initially the spring is compressed by 18 cm. The ball loses contact with the spring and leaves the gun when the spring is still compressed by 12 cm. What is the speed of the ball when it hits the ground, 1.4 m below the spring gun?

A 20-kg child wants to slide along a horizontal yard toy that consists of a slick plastic sheet covered with a thin layer of water to reduce friction to almost zero. To cause him to slide, you squirt him with a stream of water from a hose. (a) If the water from the hose exerts a constant force of 5.0 N on the child, what is the work done by the water in the interval from t = 0 to t = 1.0 s? (b) What is the instantaneous power delivered by the water at t = 1.0 s?

Explain why stepwise regression is used. What is its value in the model-building process?

Classify (if possible) each critical point of the given second-order differential equation as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. $x^{\prime \prime}+x=\epsilon x^{3}$ for $\epsilon>0$

Cite five factors that lead to scatter in measured material properties.

A 0.15-kg cart on wheels is at rest at the origin of an x axis between (but not connected to) two relaxed springs aligned along that axis. When the cart is pushed to the left of the origin, the left spring $\left( k _ { l } = 4.0 \mathrm { N } / \mathrm { m } \right)$ is compressed and exerts a force on the cart. When the cart is pushed to the right of the origin, the right spring $\left( k _ { \mathrm { r } } = 6.0 \mathrm { N } / \mathrm { m } \right)$ is compressed and exerts a force on the cart. (a) Plot the force exerted on the cart as a function of its displacement. (b) If the cart is given an initial speed of 4.0 m/s at the origin x = 0, it might be headed to the left or to the right. How far does it go in each case? (c) What is the work done on the cart as it moves from x = 0 to its extreme right position and from x = 0 to its extreme left position? Ignore any friction effects.

Assume that when you stretch your torso vertically as much as you can, your center of mass is 1.0 m above the floor. The maximum force you can exert on the floor in pushing off is 2.3 times the gravitational force Earth exerts on you. How low do you have to crouch in order to jump straight up and have your center of mass be 2.0 m above the floor? Is this crouch practical?

Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height 1.83 m. The density of blood is 1.06 × 10³ kg/m³.

The velocity-versus-time graph for a car driving down a straight road is shown in Figure Q2.27. How far does the car travel during the time interval from $t=0 \mathrm{~s}$ to $t=4.0 \mathrm{~s}$ ?
A. $10 \mathrm{~m}$
B. $20 \mathrm{~m}$
C. $40 \mathrm{~m}$
D. $60 \mathrm{~m}$

You push a blob of gelatin with a constant force of 3.0 N across a wet table on which it slides easily. Because the blob shape distorts, its center of mass moves only 30 mm during the time interval in which the point of application of your force moves 50 mm. (a) What is the work done by you on the blob? (b) By how much does your force change the kinetic energy of the center of mass?