Skip to main content
Ch. 03 - Kinematics in Two or Three Dimensions; Vectors
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 03 - Kinematics in Two or Three Dimensions; VectorsProblem 45a
Chapter 3, Problem 45a

A stunt driver wants to make his car jump over 8 cars parked side by side below a horizontal ramp (Fig. 3–46). With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the car roofs and the horizontal distance he must clear is 22 m. 
<IMAGE>

Verified step by step guidance
1
Identify the type of motion: The car undergoes projectile motion after leaving the horizontal ramp. This means we need to analyze both horizontal and vertical components of the motion separately.
Write the equations for vertical motion: The vertical displacement (Δy) is -1.5 m (negative because the car is falling downward). The initial vertical velocity (v_y0) is 0 m/s since the car leaves the ramp horizontally. Use the kinematic equation Δy = v_y0 * t + (1/2) * g * t^2 to solve for the time of flight (t), where g = 9.8 m/s².
Solve for time of flight (t): Rearrange the vertical motion equation to isolate t. This gives t = sqrt((2 * |Δy|) / g), where |Δy| is the magnitude of the vertical displacement.
Analyze horizontal motion: The horizontal velocity (v_x) remains constant throughout the motion because there is no horizontal acceleration. The horizontal displacement (Δx) is 22 m. Use the equation Δx = v_x * t to solve for the required horizontal velocity (v_x).
Combine results: Substitute the value of t (from the vertical motion equation) into the horizontal motion equation to find the minimum speed v_x. Since the car's initial velocity is purely horizontal, the minimum speed required is equal to v_x.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject to the force of gravity. It can be analyzed in two dimensions: horizontal and vertical. The horizontal motion is uniform, while the vertical motion is influenced by gravitational acceleration. Understanding the principles of projectile motion is essential for determining the trajectory and range of the stunt driver's jump.
Recommended video:
Guided course
04:44
Introduction to Projectile Motion

Kinematic Equations

Kinematic equations describe the relationships between an object's displacement, velocity, acceleration, and time. In this scenario, they can be used to calculate the minimum speed required for the car to clear the horizontal distance of 22 m while accounting for the vertical drop of 1.5 m. These equations are fundamental in solving problems involving motion under constant acceleration, such as gravity.
Recommended video:
Guided course
08:25
Kinematics Equations

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this context, the stunt driver converts kinetic energy into gravitational potential energy as the car ascends the ramp. The minimum speed required to clear the jump can be determined by equating the kinetic energy at the ramp's edge to the potential energy at the peak of the jump, ensuring the car has enough energy to complete the jump.
Recommended video:
Guided course
06:24
Conservation Of Mechanical Energy
Related Practice
Textbook Question

Two cars approach a street corner at right angles to each other (Fig. 3–57). Car 1 travels at a speed relative to Earth v₁ₑ = 35 km/h, and car 2 at v₂ₑ = 55 km/h. What is the relative velocity of car 1 as seen by car 2? What is the velocity of car 2 relative to car 1?

1
views
Textbook Question

At serve, a tennis player aims to hit the ball horizontally. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is 'launched' from a height of 2.30 m? Where will the ball land if it just clears the net (and will it be 'good' in the sense that it lands within 7.0 m of the net)? How long will it be in the air? See Fig. 3–50.

2
views
Textbook Question

A motorboat whose speed in still water is 4.30 m/s must aim upstream at an angle of 23.5° (with respect to a line perpendicular to the shore) in order to travel directly across the stream. What is the resultant speed of the boat with respect to the shore? (See Fig. 3–33.)

1
views
Textbook Question

A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). What is the vertical component of her acceleration?

<IMAGE>

1
views
Textbook Question

A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 125 m? 

<IMAGE>

2
views
Textbook Question

A diver running 2.5 m/s dives out horizontally from the edge of a vertical cliff and 3.5 s later reaches the water below. How high was the cliff and how far from its base did the diver hit the water?

1
views