A motorcycle daredevil plans to ride up a 2.0-m-high, 20° ramp, sail across a 10-m-wide pool filled with hungry crocodiles, and land at grou

Question

A motorcycle daredevil plans to ride up a 2.0-m-high, 20° ramp, sail across a 10-m-wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motor-cycle engine dies just as he starts up the ramp. He is going 11 m/s at that instant, and the rolling friction of his rubber tires (coefficient 0.02) is not negligible. Does he survive, or does he become croco-dile food? Justify your answer by calculating the distance he travels through the air after leaving the end of the ramp

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2 months 2021-07-31T23:03:14+00:00 1 Answers 2 views 0

He becomes a croco-dile food

Explanation:

From the question we are told that

The height is h = 2.0 m

The angle is

The distance is

The speed is

The coefficient of static friction is

At equilibrium the forces acting on the motorcycle are mathematically represented as

where   is the frictional force mathematically represented as

where is the horizontal component of the force

substituting into the equation

making  a the subject of the formula

substituting values

Applying ” SOHCAHTOA” rule we mathematically evaluate that length of the ramp as

making the subject

substituting values

Apply Newton equation of motion we can mathematically evaluate the  final velocity at the end of the ramp  as

The negative a means it is moving against gravity

substituting values

The initial velocity at the beginning of the pool (end of ramp) is composed of two component which is

Initial velocity along the x-axis which is mathematically evaluated as

substituting values

Initial velocity along the y-axis which is mathematically evaluated as

substituting values

Now the motion through the pool in the vertical direction can mathematically modeled as

where is the initial height,

is the initial velocity in the y-axis

is the  initial  acceleration in the y axis  with a constant value of ()

at the y= 0 which is when the height above ground is zero

Substituting values

The negative sign is because the acceleration is moving against the motion

Solving using quadratic formula

substituting values

since in this case time cannot be negative

At this time the position the  motorcycle along the x-axis is mathematically evaluated as

x

So from this value we can see that the motorcycle would not cross the pool as the position is less that the length of  the pool