a bus is moving downhill at a slope of 5 degree . at the moment when the speed of the bus is 30km/h,the driver spots a deer 30m ahead. he applies the brakes and comes to a stop. the is paralysed by fear and does not move.will the bus stops before reaching it or will it hit the deer? do relevant calculation and draw force diagram.take the coefficient of kinetic friction to be 0.26

Calculate the friction force of the skidding bus. From that and the downhill component of the weight, get the deceleration rate.

That and the initial velocity will get to the stopping distance.

Be sure to convert the 30 km/h speed to m/s before doing the calculations.

Show work for further assistance, if needed.

To determine whether the bus will stop before reaching the deer or hit it, we need to consider the forces acting on the bus, the friction force, and the distance required to stop.

Let's begin by calculating the gravitational force acting on the bus. The force due to gravity can be determined using the formula:

Force due to gravity = mass x acceleration due to gravity

The mass of the bus is not given, so we will assume a typical value of 10,000 kg.

Force due to gravity = 10,000 kg x 9.8 m/s^2
= 98,000 N

Now, let's determine the friction force acting on the bus. The formula for friction force is:

Friction force = coefficient of friction x normal force

The normal force can be found using the formula:

Normal force = mass x gravitational acceleration - mass x acceleration due to gravity x sin(theta)

Where:
mass = mass of the bus (10,000 kg)
gravitational acceleration = 9.8 m/s^2
theta = slope angle (5 degrees)

Normal force = 10,000 kg x 9.8 m/s^2 - 10,000 kg x 9.8 m/s^2 x sin(5 degrees)
= 10,000 kg x 9.8 m/s^2 - 10,000 kg x 9.8 m/s^2 x 0.087
= 10,000 kg x 9.8 m/s^2 (1 - 0.087)
= 10,000 kg x 9.8 m/s^2 x 0.913
≈ 89,410 N

Now, we can calculate the friction force:

Friction force = 0.26 x 89,410 N
≈ 23,234 N

Next, let's determine the deceleration of the bus. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

Net force = mass x acceleration

The net force can be determined using the formula:

Net force = Force due to gravity - Friction force

Acceleration = Net force / mass
= (Force due to gravity - Friction force) / mass

Acceleration = (98,000 N - 23,234 N) / 10,000 kg
≈ 7.76 m/s^2

Now, let's calculate the distance required to stop:

We can use the following kinematic equation:

v^2 = u^2 - 2as

Where:
v = final velocity (0 m/s as the bus comes to a stop)
u = initial velocity (30 km/h = 8.33 m/s)
a = acceleration (-7.76 m/s^2)
s = distance

0^2 = (8.33 m/s)^2 - 2(-7.76 m/s^2)s

Rearranging the equation:

-64.96 m/s^2 s = (8.33 m/s)^2

s = ((8.33 m/s)^2) / 64.96 m/s^2
s ≈ 1.07 m

The calculated distance required to stop is approximately 1.07 meters.

Considering that the driver spots the deer 30 meters ahead and the bus will stop in 1.07 meters, we can conclude that the bus will stop before reaching the deer.