A security guard is chasing a burglar across a rooftop, both...

A security guard is chasing a burglar across a rooftop, both running at $4.2 \mathrm{~m} / \mathrm{s}$. Before the burglar reaches the edge of the roof, he has to decide whether or not to try jumping to the roof of the next building, which is $5.5 \mathrm{~m}$ away and $4.0 \mathrm{~m}$ lower. If he decides to jump horizontally to get away from the guard, can he make it? Explain your answer.

Key Concepts

Projectile Motion

Projectile motion involves the motion of an object that is launched into the air and then moves under the influence of gravity. The analysis divides the motion into horizontal and vertical components, allowing one to predict the trajectory, range, and time in the air of the projectile.

Free-fall Kinematics

Free-fall kinematics refers to the motion of objects under the influence of gravity alone. It involves using equations of motion to calculate variables such as displacement, velocity, and time, assuming a constant acceleration due to gravity acting downward.

Horizontal Launch

In a horizontal launch scenario, an object is given an initial horizontal velocity with no initial vertical component. This simplification allows the vertical motion to be analyzed solely as a free-fall problem, while the horizontal motion remains at a constant speed, making it easier to calculate the distance traveled during the time of flight.

Time of Flight Calculation

The time of flight is determined by analyzing the vertical displacement using free-fall kinematics. By calculating the time it takes for an object to fall a certain height under gravity, one can then use the horizontal velocity to find the total horizontal distance traveled during this time. This calculation is crucial in determining whether a horizontally launched projectile can cover a required distance.

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