An African swallow carrying a very small coconut is flying horizontally with a speed of 18 m/s. (a) If it drops the coconut from a height of 100 m above the Earth, how long will it take before the coconut strikes the ground? (b) At what horizontal distance from the release point will the coconut strike the ground?

Let $I$ be an arbitrary nonempty index set and for each $i \in I$ let $N_{i}$ be a left $R$ -module. Let $M$ be a right $R$ -module. Prove the group isomorphism: $M \otimes\left(\oplus_{i \in I} N_{i}\right) \cong \oplus_{i \in I}\left(M \otimes N_{i}\right)$ where the direct sum of an arbitrary collection of modules is defined in Exercise 20 , Section $3 .$ IUse the same argument as for the direct sum of two modules, taking care to note where the direct sum hypothesis is needed - cf. the next exercise. $.$ .

A cannonball is catapulted toward a castle. The cannonball's velocity when it leaves the catapult is 40 m/s at an angle of

$$37 ^ { \circ }$$

with respect to the horizontal and the cannonball is 7.0 m above the ground at this time. (a) What is the maximum height above the ground reached by the cannonball? (b) Assuming the cannonball makes it over the castle walls and lands back down on the ground, at what horizontal distance from its release point will it land? (c) What are the x- and y-components of the cannonballs velocity just before it lands? The y-axis points up.

The coefficient of static friction between a block and a horizontal floor is 0.40, while the coefficient of kinetic friction is 0.15. The mass of the block is 5.0 kg. A horizontal force is applied to the block and slowly increased. (a) What is the value of the applied horizontal force at the instant that the block starts to slide? (b) What is the net force on the block after it starts to slide?

Find the sum of the Interior angle measures of each polygon. 14-gon

A 10-V independent voltage source is in series with a 2-A independent current source. What single source is equivalent to this series combination? Give the type and value of the equivalent source.

The CMB contains roughly 400 million photons per $\mathrm{m}^{3}$. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien’s law, the peak wave length in nanometers is given by $\lambda \max =\lambda_{\max }=\frac{3 \times 10^{6}}{T}$. Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters.

A rope is attached from a truck to a 1400 kg car. The rope will break if the tension is greater than 2500 N. Ignoring friction, find the maximum possible acceleration of the truck if the rope does not break. Should the driver of the truck be concerned that the rope might break?

Write each percent-as a fraction and.as a decimal.

$$\frac{3}{4}\%$$

Let

$$\mathbf{v}_{1}=(1,7,-3), \mathbf{v}_{2}=(2,1 ,4), \mathbf{v}_{3}=(6,5,1), \mathbf{v}_{4}=(0,7 ,13)$$

Determine whether or not the given vectors in $R^n$ form a basis for $R^n$.

As a tennis ball is struck, it departs from the racket horizontally with a speed of 28.0 mis. The ball hits the court at a horizontal distance of 19.6 m from the racket. How far above the court is the tennis ball when it leaves the racket?

The tennis ball is struck with a horizontal velocity $v_A$, strikes the smooth ground at B, and bounces upward at$\theta = 30^{\circ}$. Determine the initial velocity $v_A$, the final velocity $v_B$, and the coefficient of restitution between the ball and the ground.

A helicopter is Lifting two crates simultaneously. One crate with a mass of 200 kg is attached to the helicopter by a cable. The second crate with a mass of 100 kg is hanging below the first crate and attached to the first crate by a cable. As the helicopter accelerates upward at a rate of 1.0

$$m/s^2$$

, what is the tension in each of the two cables?

Describe the kind of life Walker's mother led while Walker was growing up.