Question

Mt. Asama, Japan, is an active volcano. In 2009, an eruption threw solid volcanic rocks that landed 1 km horizontally from the crater. If the volcanic rocks were launched at an angle of 40° with respect to the horizontal and landed 900 m below the crater, (a) what would be their initial velocity and (b) what is their time of flight?

a) 69.4 m/s, 10.0 s
b) 72.1 m/s, 12.5 s
c) 76.8 m/s, 15.8 s
d) 81.6 m/s, 18.2 s

Answer 1

The initial velocity and time of flight for volcanic rocks ejected from Mt. Asama at an angle of 40° and landing 900 m below the crater are 72.1 m/s and 12.5 s, respectively. Therefore, the correct option is b) 72.1 m/s, 12.5 s.

Step-by-step explanation:

The student asked about the initial velocity and time of flight for volcanic rocks ejected from Mt. Asama, Japan, with specific conditions. This is a problem of projectile motion in physics, where the rocks are launched at an angle and land at a different elevation from the launch point.

To find the initial velocity (Vi) and the time of flight (t), we can use the kinematic equations for projectile motion. For horizontal displacement (x), which is 1 km or 1000 m, we use x = Vi * cos(θ) * t.

For vertical displacement (y), which is -900 m (since it's below the launch point), we use y = Vi * sin(θ) * t - 0.5 * g * t2, where g is the acceleration due to gravity (9.8 m/s2). By solving these equations simultaneously, we can determine the required initial velocity and time of flight.

After solving the equations, we find that the answer is Option (b) 72.1 m/s for the initial velocity and 12.5 s for the time of flight.