Question

Bird Watching 2 You are looking up and tracking a bird's steady horizontal motion. The bird is 35 m above the ground and moving at 6 m/s. Write an expression for the angle of your head as a function of time ( t ). Assume the bird is directly overhead at t=0. Write the expression for the angle of your gaze from the vertical, so that zero radians (or degrees) represents looking straight up, and π/2 radians (90deg) is looking horizontal.

Answer 1

The question involves calculating the horizontal position of a mouse after being dropped by an owl, using principles of projectile motion in Physics. By finding the time for the mouse to fall 12.0 m and applying it to the constant horizontal speed of the owl, we can ascertain if the mouse lands in the nest.

Step-by-step explanation:

When a student asks about calculating the horizontal position of a mouse dropped by an owl, they are dealing with a problem in projectile motion within the context of Physics. To determine whether the mouse hits the nest, you must consider the horizontal and vertical components of the motion separately.

Given that the owl is flying east at 3.50 m/s and the initial position of the mouse is 4.00 m west of the nest, we first need to find the time it takes for the mouse to fall 12.0 m. Assuming there is no air resistance and using the acceleration due to gravity which is approximately 9.81 m/s2, we can use the equation for the vertical motion (d = 1/2 * g * t2) to find the time.

After finding the time, we apply it to the horizontal motion. Since the owl is flying horizontally at a constant speed, we can use the equation (horizontal distance = speed * time) to find the horizontal position of the mouse when it has fallen the 12.0 m. If the horizontal position is within plus or minus 15 cm of the nest center, considering the nest's diameter is 30.0 cm, the mouse will hit the nest.