Q: A child is running at her maximum speed of 4.0 m/s to catch an ice-cream...

Q: A child is running at her maximum speed of 4.0 m/s to catch an ice-cream truck, which is stopped at the side of the road. When the child is 20 m from the truck, the ice-cream truck starts to accelerate away at a rate of 1.0 m/s² . Does the child catch the truck? solve this problem algebraically and graphically.

Expert Solution

Algebraic method :
Let the velocity of the child is v = 4.0 m/s. And the acceleration of the ice cream truck is a = 1.0 m/s^2.
And as there is an initial gap d = 20 m, so, we have at time t, the distance travelled by the child is

And similarly, the distance travelled by the ice cream truck is

And the child will be able to catch the truck if at the time t the child also cover the extra initial distance between the child and the truck. So, the condition is


  And so, we get



Now in the given case,

And so,

So, the time is imaginary. So, this implies that the child will never be able to catch the truck.

Graphically :
  We plot the two functions

And

on the same plot. And this implies

And the two plots implies that they will not intersect at any finite time t. And so, we see that the child will not be able to catch the truck.

genius_generous answered 2 years ago

A student is running at her top speed of 5m/s to catch a bus, which is...

A student is running at her top speed of 5m/s to catch a bus, which is stopped at a bus stop. When the student is still 80m behind the bus, it starts to pull away, moving with a constant acceleration of 0.1m/s2. (a) How much time will be needed for student to catch the bus? (b) What distance does the student have to run before she catches the bus? (c) When she reaches the bus, how fast is the bus...

The maximum speed of a child on a swing is 5.90 m/s. The child’s height above...

The maximum speed of a child on a swing is 5.90 m/s. The child’s height above the ground is 0.790 m at the lowest point in his motion. How high above the ground is he at his highest point? m

Sprinter Usain Bolt reached a maximum speed of 11.2 m/s in 2.0s while running 100-m dash....

Sprinter Usain Bolt reached a maximum speed of 11.2 m/s in 2.0s while running 100-m dash. A) what was his acceleration? B) What distance did he travel during his first 2.0s of the race? C) What assumptions did you make? D) What time interval was needed to complete the race assuming that he ran the last part of the race at his maximum speed? E) what is the total time of the race? How certain are you of the number...

Anita is running to the right with a speed of 6 m/s

Anita is running to the right with a speed of $6.0 \mathrm{~m} / \mathrm{s}$, as shown in the figure. Balls 1 and 2 are thrown toward her by her friends (standing still on the ground). As measured by Anita, both balls are approaching her at a speed of $11 \mathrm{~m} / \mathrm{s}$.You may assume all the motions are completely horizontal.a) According to her friends, what is the magnitude and direction of the velocity of ball $1\left(\vec{v}_{1}\right) ?$b) According to her...

A man is running at speed c (much less than the speed of light) to catch...

A man is running at speed c (much less than the speed of light) to catch a bus already at a stop. At t=0, when he is a distance b from the door to the bus, the bus starts moving with the positive acceleration a. Use a coordinate system with x=0 at the door of the stopped bus. a) What is xman(t), the position of the man as a function of time? Answer symbolically in terms of the variables b,...

A 34kg child runs with a speed of 2.4 m/s tangential to the rim of a...

A 34kg child runs with a speed of 2.4 m/s tangential to the rim of a stationary merry go round. The merry go round has a moment of inertia of 520 kg*m^2 and a radius of 2.00m. After the child hops on the merry go round it rotates with an angular speed of 0.3 rad/s. Find the initial and final kinetic energy of the system. (merry go round and the child). If a frictional torque of 340 is present to...

A child rides down the road on his bike at a speed 4.3 m/s with a...

A child rides down the road on his bike at a speed 4.3 m/s with a balloon tied to its handle bars. At a time t = 0 s, the balloon comes untied and floats into the air. It accelerates with the vector: a(t) = ( -0.31 m/s2 e(-0.072093 s-1 t ) , 4.71 m/s2 - 0 m/s3 t ) [Note: The acceleration coefficient in the x-direction should be v0? (= -0.3099 m/s2) where v0 is the initial speed and...

A ball is thrown upward with a speed of 28.2 m/s. A. What is its maximum...

A ball is thrown upward with a speed of 28.2 m/s. A. What is its maximum height? B. How long is the ball in the air? C. When does the ball have a speed of 12m/s? (there are two answers, give both)

A (field) hockey player is running north at a speed of 8 m⋅s−1. A ball is...

A (field) hockey player is running north at a speed of 8 m⋅s−1. A ball is coming directly towards her from the north at a speed of 18 m⋅s−1. She swings her stick forward, directly north, at a speed of 6 m⋅s−1 measured in her own frame of reference. What is the speed of the ball with respect to the hockey stick? Relative to the hockey stick, the ball is travelling at ____ m⋅s−1. Jane's brother Andrew leaves home for...

The Billy Ice Cream Company pays a constant dividend. Last year, the dividend yield was 4.0...

The Billy Ice Cream Company pays a constant dividend. Last year, the dividend yield was 4.0 percent when the stock was selling for $16 a share. a) What must the stock price be today if the market currently requires a 4.3 percent dividend yield on this stock? b) If the total required return of this stock equals 8.9%, what should investors require as growth rate?

Question