Final answer:
The vertical speed of a kangaroo when it leaves the ground to clear a 2.50 m object is calculated using the equation v_y = sqrt(2gh), which stems from energy conservation. The time in air can be found by applying kinematic equations for projectile motion.
Step-by-step explanation:
To calculate the vertical speed of a kangaroo when it leaves the ground to jump over an object 2.50 m high, we can use the kinematic equation related to the conservation of energy. The formula vy = sqrt(2gh) is derived from the principle that the kinetic energy imparted to the kangaroo at takeoff is converted to gravitational potential energy at the peak of its jump, where its velocity is zero. Here, g is the acceleration due to gravity (9.8 m/s2), and h is the height (2.50 m).
To find the time the kangaroo is in air, you can use the kinematic equations for projectile motion, which divide the motion into upwards and downwards parts, considering that the time to reach the peak height is the same as the time to fall back down from the peak.