Chapter 2, Problem 64P

A student standing on a cliff that is a vertical height d d = 25 ft above the level ground throws a stone with velocity v0 v 0 = 59 ft/s at an angle θ θ = 18 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position. With what speed, vfvf in feet per second, does the stone strike the ground

A particle’s acceleration is (4.0iˆ+3.0jˆ)m/s2.(4.0i^+3.0j^)m/s2. At t = 0, its position and velocity are zero. (a) What are the particle’s position and velocity as functions of time? (b) Find the equation of the path of the particle. Draw the x- and y-axes and sketch the trajectory of the particle.

On a planet very similar to Earth, but slightly denser, where acceleration due to gravity is 10 m/s2, a projectile is fire vertically from a height of 100 meters with an initial velocity of 40 m/s. Its position above the ground after t seconds is given by h(t) = 100 + 40t − 5t2 meters. Find the maximum height the projectile attains.

Starting from rest, the motorboat travels around the circular path, ρ = 50 m, at a speed v=(0.2t^2)m/s, where t is in seconds. (Figure 1) A) Determine the magnitude of the boat's velocity at the instant t = 3 s. Express your answer to three significant figures and include the appropriate units.   B)Determine the magnitude of the boat's acceleration at the instant t = 3 s. Express your answer to three significant figures and include the appropriate units.

The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 1.36 m above the floor. The ball hits the floor 0.316 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)? 1 13.6 m/s^2 2 20.4 m/s^2 54.4 m/s^2 4 27.2 m/s^2

A cannon is on a cliff (on Earth). It fires a cannonball. The cannonball must reach its peak exactly 10m above the original height of the cliff. (a) Choose values for the following. None of them can be 0. The launch velocity (speed and angle) of the cannonball. The height of the cliff (b) Draw a picture. (c) Label the origin and axes. (d) Calculate all kinematics variables in x and y between launch and peak. (e) Calculate all kinematics variables in x and y between launch and land.

т A cannon sits on a horizontal plain, angled up at 35°. A cannonball is fired with a velocity of 100“. The cannonball hits the ground at the same height from which it was launched. a) What is the maximum height of the cannonball? (Answer: 168 m ) b) What is the flight time of the cannonball? (Answer: 11.7 s) c) What is the horizontal range of the cannonball? (Answer: 959 m) d) What is the impact velocity in magnitude and angle? (Answer: 100@35° below x-axis)

Q.4. A robot lands on Mars. Its x and y coordinates are given by equations:x(t) = 2m –(0.25m/s2)t2y(t)= (1.0 m/s)t +(0.025m/s3) (a).What is the position and distance from landing at t=2 seconds?(b)What is thedisplacement and average velocity during the interval from t=0 s to t= 2?(c).Derivea general expression for its instantaneous velocity vector and find its instantaneousvelocity in its component form as well as in terms of its magnitude.

A diver jumps off a cliff of height h at an angle θ = 260 (see figure). He reaches a maximum height of h subscript m a x end subscript= 20 m above the top of the cliff before falling to the water below. He hits the water x=295 m from the base of the cliff. Determine the height of the cliff, h. Take g=10m/s2 . Round your answer to one decimal place.