Question

When chasing a hare along a flat stretch of ground, a greyhound leaps into the air at a speed of 8.10 m/s, at an angle of 32.0∘

above the horizontal.
(a) What is the range of his leap and

Answer 1

The range of the greyhound's leap is 6.04 meters.

Step-by-step explanation:

The range of the leap can be calculated using the horizontal component of the greyhound's initial velocity. The horizontal component is given by:

Horizontal component = Initial velocity * cos(angle)

Substituting the given values:

Horizontal component = 8.10 m/s * cos(32.0°)

Calculating the horizontal component:

Horizontal component = 8.10 m/s * 0.848

Horizontal component = 6.87 m/s

The time of the leap can be calculated using the vertical component of the greyhound's initial velocity. The vertical component is given by:

Vertical component = Initial velocity * sin(angle)

Substituting the given values:

Vertical component = 8.10 m/s * sin(32.0°)

Calculating the vertical component:

Vertical component = 8.10 m/s * 0.529

Vertical component = 4.29 m/s

The time of the leap can be calculated using the equation:

Time = (2 * Vertical component) / acceleration due to gravity

Substituting the values:

Time = (2 * 4.29 m/s) / 9.8 m/s^2

Calculating the time:

Time = 0.877 seconds

Finally, the range of the leap can be calculated using the equation:

Range = Horizontal component * Time

Substituting the values:

Range = 6.87 m/s * 0.877 seconds

Calculating the range:

Range = 6.04 meters