1)A hiker throws a ball at an angle of 21.0 above the horizontal from a hill 21.0 m high. The hiker's height is 1.750 m. The magnitudes of the horizontal and vertical components are 14.004 m/s and 5.376 m/s, respectivley. Find the distance between the base of the hill and the point where the ball hits the ground. (Consider the hiker's height while calculating the answer.)

just te1l me what direction to go in please.

2)A car of mass 1330 kg is traveling at 28.0 m/s. The driver applies the brakes to bring the car to rest over a distance of 79.0 m. Calculate the retarding force acting on the car.

(79.0/28.0)*1330
3752.5

Assume the ball starts its upward flight from the top of the throwers head, 1.75m above the ground.

1--Time to maximum height above the thrower's head derives from Vf = Vo - 9.8t or 0 = 5.376 - 9.8t making t(up) = .548sec.
2--Time back to the top of the throwers head is also .548sec. and the velocity the same as the departure velocity, 5.376m/s.
3--The time to reach the ground from the height of 21 + 1.75 = 22.75m = Vot + 9.8t^2/2 or 4.9t^2 + 5.376t - 22.75 = 0.
4--Solve for t using the quadratic formula.
5--Having t, the horizontal distance traveled becomes 14.004(.548 + .548 + t)

15.3

1) To find the distance between the base of the hill and the point where the ball hits the ground, we can break down the problem into horizontal and vertical components.

Given the angle and the magnitudes of the horizontal and vertical components of the ball's velocity, we can use trigonometry to find the time of flight for the ball.

The horizontal component of the ball's velocity remains constant throughout its motion since there is no horizontal acceleration. The vertical component, however, experiences acceleration due to gravity.

To find the time of flight, we can use the equation:

time = (2 * vertical component of initial velocity) / acceleration due to gravity

Substituting the given values, we have:

time = (2 * 5.376 m/s) / 9.8 m/s^2

Simplifying, we find:

time = 1.0964 seconds

Now, we can find the horizontal distance travelled by the ball using the equation:

horizontal distance = horizontal component of initial velocity * time

Substituting the given values, we have:

horizontal distance = 14.004 m/s * 1.0964 s

Simplifying, we find:

horizontal distance = 15.34 meters

To account for the hiker's height, we add the height of the hill (21.0 m) to the final calculated horizontal distance:

total distance = horizontal distance + hiker's height

Substituting the values, we have:

total distance = 15.34 m + 21.0 m

Simplifying, we find:

total distance = 36.34 meters

Therefore, the distance between the base of the hill and the point where the ball hits the ground, accounting for the hiker's height, is 36.34 meters.

2) To calculate the retarding force acting on the car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

Given that the car's mass is 1330 kg and it comes to rest over a distance of 79.0 m with an initial velocity of 28.0 m/s, we can calculate the deceleration of the car using the formula:

acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)

Substituting the given values, we have:

acceleration = (0 - (28.0 m/s)^2) / (2 * 79.0 m)

Simplifying, we find:

acceleration = -0.5 m/s^2 (Note the negative sign indicates deceleration)

Now, we can calculate the net force acting on the car using the formula:

net force = mass * acceleration

Substituting the given values, we have:

net force = 1330 kg * -0.5 m/s^2

Simplifying, we find:

net force = -665 N

Therefore, the retarding force acting on the car is 665 Newtons, in the opposite direction to its motion.