A child drops a toy with a mass of 200 g from the balcony of a building 20 m as tall as he is, vertically starting from rest. Assume that the force of air resistance is proportional to the instantaneous speed of the toy, which takes 3 s to hit the ground. If the acceleration due to gravity is 9.8 m/s2 (a) Write a differential equation and the conditions to determine the position of the toy in any instant t. (b) Determine the equation of motion of the toy. (c) Find the limit speed of the toy.

A child drops a toy with a mass of 200 g from the balcony of a building 20 m as tall as he is, vertically starting from rest. Assume that the force of air resistance is proportional to the instantaneous speed of the toy, which takes 3 s to hit the ground. If the acceleration due to gravity is 9.8 m/s2 (a) Write a differential equation and the conditions to determine the position of the toy in any instant t. (b) Determine the equation of motion of the toy. (c) Find the limit speed of the toy.

Name: A child drops a toy with a mass of 200 g from the balcony of a buildi
Uploaded: 2024-03-20T06:57:57.000Z
Channel: Bartleby
Description: A child drops a toy with a mass of 200 g from the balcony of a building 20 m astall as he is, vertically starting from rest. Assume that the force of air resistanceis proportional to the instantaneous speed of the toy, which takes 3 s to hit thegrou

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter6: Motion In Two Dimensions

Section: Chapter Questions

Problem 7STP

See similar textbooks

Similar questions

A car is moving on a flat road with a constant velocity of 40.0 m/s. The car has a mass of 1500. kg. The driver releases the gas pedal and the car glides to rest over a distance of 395 m. Find: (a) The acceleration of the car during the "glide" (b) The resultant force acting on the car. (c) What are the forces that cause the car to decelerate?
The acceleration on a falling tennis ball is not constant due to air resistance. The time dependent acceleration is given by ?*e^-bt, where b is some constant related to the drag coefficient of friction in air and mass of the ball. What is the velocity of the ball at time t, assuming it starts from rest at t=0?
An elevator in the Taipei 101 skyscraper can start fromrest and accelerate to a maximum speed of 16 m>s with a constantacceleration of 1.1 m>s2. Through what distance does the elevatormove as it accelerates to its maximum speed?
A parachutist is falling with his open parachute. Does he experience a constant acceleration? why or why not
The pilot of a jet transport brings the engines to full takeoff power before releasing the brakes as the aircraft is standing on the runway. The jet thrust remains constant, and the aircraft has a near-constant acceleration of 0.44g. If the takeoff speed is 150 km/h, calculate the distance s and time t from rest to takeoff. Ans: s = _____ m t = _____ s
When an object is released from rest and falls in the absence of friction, which of the following is true concerning its motion? A. Both its acceleration and its velocity are constant B. Neither its acceleration nor its velocity is constant C. Its acceleration is constant D. Its velocity is constant
A model rocket is fired from the roof of a 50 ft. tall building as shown in the figure below. The height of the rocket is given by: y(t) = 150t - 16.1t2+ 50ft Find the following. a) The velocity v(t) = dy/dt as well as the initial velocity v0 = v(0) b) The acceleration a(t) = dv/dt c) The time required to reach the maximum height as well as the corresponding height ymax
If a car is traveling due westward with a constant speed of 20 m/s, what is the resultant force acting on it?
A body falls freely from rest. a. the distance it falls in 3 s, b) its speed after falling 70 m, c) the time required to reach a speed of 25 m/s, and e) the time taken to fall 300 m.
At a given instant in time, a 7-kg rock that has been dropped from a high cliff experiences a force of air resistance of 25 N. What are the magnitude and direction of the acceleration of the rock? (Do not forget the gravitational force!)
A body moves on a coordinate line such that it has a position s=f(t)=t2−8t+7 on the interval 0≤t≤7, with s in meters and t in seconds. a. Find the body's displacement and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval. c. When, if ever, during the interval does the body change direction?
From a great height, a mass of m = 20 kg was dropped onto the Earth. Assuming that the force of air resistance to the movement of the load varies in proportion to the speed, determine after what time interval Δt the acceleration of the movement of the load will be equal to one third of the acceleration of gravity. (Coefficient of resistance to movement k = 10 kg / s).