During volcanic eruptions, chunks of solid rock

can be blasted out of the volcano; these projectiles
are called volcanic bombs. The Figure shows a
cross section of Mt. Fuji, in Japan.
(a) At what initial speed would a bomb have to
be ejected, at angle q0 = 35° to the
horizontal, from the vent at A in order to fall at the foot of the volcano at B, at vertical
distance h = 3.30 km and horizontal distance d = 9.40 km? Ignore the effects of air on the
bomb's travel.
(b) What would be the time of flight

I did this a few days ago.

http://www.jiskha.com/display.cgi?id=1451329598

To solve this problem, we can use the principles of projectile motion. We can break down the motion of the volcanic bomb into vertical and horizontal components.

(a) To find the initial speed required, we need to calculate the initial velocity components in the horizontal and vertical directions separately.

Let's consider the vertical motion first. The vertical displacement is given as h = 3.30 km. Using the equation for vertical displacement in projectile motion:

h = (v0^2 * sin^2(q0)) / (2 * g)

where:
v0 = initial velocity (we need to find this)
q0 = launch angle (given as 35°)
g = acceleration due to gravity (9.8 m/s^2)

Rearranging the equation, we can find the initial velocity v0:

v0 = sqrt(2 * g * h / sin^2(q0))

Substituting the given values:

v0 = sqrt(2 * 9.8 m/s^2 * 3.30 km / sin^2(35°))

Remember to convert the vertical distance h from km to m:

v0 = sqrt(2 * 9.8 m/s^2 * 3.30 * 10^3 m / sin^2(35°))

Now, let's calculate the horizontal component of velocity. The horizontal distance d is given as 9.40 km. The horizontal velocity remains constant during the entire flight, so we can simply use the formula:

d = v0 * cos(q0) * t

where t is the time of flight (which we need to find).

Rearranging the equation, we can calculate the time of flight:

t = d / (v0 * cos(q0))

Substituting the given values:

t = (9.40 km) / (v0 * cos(35°))

Remember to convert the horizontal distance d from km to m:

t = (9.40 * 10^3 m) / (v0 * cos(35°))

(b) To calculate the time of flight, substitute the value of v0 into the equation for t:

t = (9.40 * 10^3 m) / (sqrt(2 * 9.8 m/s^2 * 3.30 * 10^3 m / sin^2(35°)) * cos(35°))

Now, you can calculate the time of flight by evaluating this equation using a calculator or a mathematical software.