Question

A stunt man jumps horizontally from a building to the roof of a garage that is 2 meters lower. How fast does he need to be to land on the roof of the said garage that is 3 meters away from the building?

262

likes1310 views

Eliseo

4.6

87 Answers

To solve this problem, we can use the principles of kinematics and the equation of motion.

Let's assume the initial velocity of the stunt man isv_0 and the time taken to reach the roof of the garage is t . Since the stunt man is jumping horizontally, the vertical component of his velocity is zero.

The horizontal distance traveled (d ) is given as 3 meters and the vertical distance (h ) is 2 meters.

Using the equation of motion for vertical motion:

h = \frac{1}{2}gt^2

Since the initial vertical velocity is zero, the term involvingv_0 disappears.

Simplifying the equation:

2 = \frac{1}{2} \cdot 9.8 \cdot t^2

2 = 4.9 \cdot t^2

t^2 = \frac{2}{4.9}

t^2 \approx 0.4082

Taking the square root of both sides:

t \approx 0.6397 seconds

Now, using the equation of motion for horizontal motion:

d = v_0 \cdot t

Substituting the given values:

3 = v_0 \cdot 0.6397

v_0 = \frac{3}{0.6397}

v_0 \approx 4.69 m/s

Therefore, the stunt man needs to be traveling at approximately 4.69 m/s horizontally to land on the roof of the garage.

\textbf{Answer:} The stunt man needs to be traveling at approximately 4.69 m/s horizontally.

Let's assume the initial velocity of the stunt man is

The horizontal distance traveled (

Using the equation of motion for vertical motion:

Since the initial vertical velocity is zero, the term involving

Simplifying the equation:

Taking the square root of both sides:

Now, using the equation of motion for horizontal motion:

Substituting the given values:

Therefore, the stunt man needs to be traveling at approximately 4.69 m/s horizontally to land on the roof of the garage.

\textbf{Answer:} The stunt man needs to be traveling at approximately 4.69 m/s horizontally.

Frequently asked questions (FAQs)

Question: In a circle with center O, if angle AOB is 120° and angle COB is 30°, find the measure of angle CAB.

+

What is the product of the sum of two integers, x and y, with the sum formula (x+y)^2?

+

What is the product of the sum of x and y, squared, when x = 3 and y = 5?

+

New questions in Mathematics