91Ó°ÊÓ

Given that \(\mathbf{r}(t)=\left\langle e^{-5 t} \sin t, e^{-5 t} \cos t, 4 e^{-5 t}\right\rangle\) is the position vector of a moving particle, find the following quantities: The speed of the particle

Given that \(\mathbf{r}(t)=\left\langle e^{-5 t} \sin t, e^{-5 t} \cos t, 4 e^{-5 t}\right\rangle\) is the position vector of a moving particle, find the following quantities: The acceleration of the particle

Find the maximum speed of a point on the circumference of an automobile tire of radius \(1 \mathrm{ft}\) when the automobile is traveling at \(55 \mathrm{mph}\).

A projectile is shot in the air from ground level with an initial velocity of \(500 \mathrm{~m} / \mathrm{sec}\) at an angle of \(60^{\circ}\) with the horizontal. The graph is shown here: . At what time does the projectile reach maximum height?

A projectile is shot in the air from ground level with an initial velocity of \(500 \mathrm{~m} / \mathrm{sec}\) at an angle of \(60^{\circ}\) with the horizontal. The graph is shown here: At what time is the maximum range of the projectile attained?

A projectile is shot in the air from ground level with an initial velocity of \(500 \mathrm{~m} / \mathrm{sec}\) at an angle of \(60^{\circ}\) with the horizontal. The graph is shown here: What is the total flight time of the projectile?

A projectile is fired at a height of \(1.5 \mathrm{~m}\) above the ground with an initial velocity of \(100 \mathrm{~m} / \mathrm{sec}\) and at an angle of \(30^{\circ}\) above the horizontal. Use this information to answer the following questions: Determine the maximum height of the projectile.

A projectile is fired at a height of \(1.5 \mathrm{~m}\) above the ground with an initial velocity of \(100 \mathrm{~m} / \mathrm{sec}\) and at an angle of \(30^{\circ}\) above the horizontal. Use this information to answer the following questions: Determine the range of the projectile.

A projectile is fired from ground level at an angle of \(8^{\circ}\) with the horizontal. The projectile is to have a range of \(50 \mathrm{~m}\). Find the minimum velocity necessary to achieve this range.

Prove that an object moving in a straight line at a constant speed has an acceleration of zero.