
Actually Welcome to the Concept of the Projectile Motion.
Since, here given that, vertical velocity= 50m/s
we know that u*sin(theta) = vertical velocity
so the time taken to reach the maximum height or the time of Ascent is equal to
T = Usin(theta) ÷ g, here g = 9.8 m/s^2
so we get as,
T = 50/9.8
T = 5.10 seconds
thus the time taken to reach max height is 5.10 seconds.
Answer:

Explanation:
given,
frequency of tuba.f = 64 Hz
Speed of train approaching, v = 8.50 m/s
beat frequency = ?
using Doppler's effect formula

v_s is the velocity of the source
v is the speed of sound, v = 340 m/s
now,

f' = 65.64 Hz
now, beat frequency is equal to



hence, beat frequency is equal to 1.64 Hz
If you are asking for a proof on having at least 3 dimensions in space, you can find the physical proof anywhere in your daily life activities. Just the fact that solids have volumes is a proof already that we live in a three-dimensional space. We can move forwards, backwards, sidewards and in all other directions possible.
When you go right into detail, the fundamental laws governing these proofs are very technical. They have differential equations to show as proof. It is too detailed to discuss here. The important things is that, these fundamental laws are what explains the science in our basic activities and natural phenomena:
*Gravitation and planetary motion
* Translation, rotation, magnetic field, forces
* Integrals of equations:
Heat your answer is Heat.
Hoped I helped.