Question

Measurements made in 1910 indicate that the common flea is an impressive jumper, given its size. assume that a flea’s initial speed is 2.2 m/s, and that it leaps at an angle of 21° with respect to the horizontal. if the jump lasts 0.16 s, what is the magnitude of the flea’s horizontal displacement? how high does the flea jump?

Answer 1

The horizontal displacement and height of the flea's jump can be calculated using projectile motion equations by breaking the initial velocity into horizontal and vertical components and using the time of the jump.

Step-by-step explanation:

To determine the horizontal displacement and height of the flea's jump with an initial speed of 2.2 m/s at an angle of 21°, we use the equations for projectile motion. First, we break the velocity into horizontal (vx) and vertical (vy) components:

• vx = v * cos(θ) = 2.2 * cos(21°)
• vy = v * sin(θ) = 2.2 * sin(21°)

The horizontal displacement (x) can be found using x = vx * t, where t is the duration of the jump (0.16 seconds).

For the maximum height (y), we use the vertical motion equation y = vy * t - ½ * g * t2. Here, g is the acceleration due to gravity (9.8 m/s2), and t is the time to reach the peak of the jump. Since the total time of the jump is 0.16 seconds, and the upward and downward journeys are symmetrical, the time to reach the peak is half the total time, or 0.08 seconds.

The calculations will yield the magnitude of the flea’s horizontal displacement and the height of the flea’s jump.