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a) The horizontal component of the velocity is 7.4 m/s
b) The vertical component of the velocity is 3.8 m/s
c) The balloon reaches the highest point after 0.39 s
d) The maximum height is 0.74 m
e) The total time of flight is 0.78 s
f) The range of the balloon is 5.77 m
Explanation:
a)
The motion of the balloon is the motion of a projectile, which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction
The horizontal component of the velocity (which is constant) is given by
where
u = 8.3 m/s is the initial velocity of the balloon
is the angle of projection
Substituting,
b)
The vertical component of the initial velocity of a projectile is given by
where
u is the initial velocity
is the angle of projection
Here we have
u = 8.3 m/s
Substituting,
c)
The vertical component of the velocity of the balloon follows the suvat equation
where
is the vertical velocity at time t
is the initial vertical velocity
is the acceleration of gravity
The balloon reaches the maximum height when the vertical velocity becomes zero:
So we get:
d)
The maximum height of the balloon can be calculated using the suvat equation:
where
is the initial vertical velocity
is the acceleration of gravity
t = 0.39 s is the time at which the highest point is reached
Substituting,
e)
The total time of flight of a projectile is twice the time needed to reach the maximum height, and it is given by
where
is the initial vertical velocity
is the acceleration of gravity
Here we have
Substituting,
f)
The range of a projectile is the horizontal distance covered by the projectile, so it can be found by multiplying its horizontal velocity (which is constant) by the time of flight:
where
is the horizontal velocity
t is the time of flight
Here we have
Substituting,
Learn more about projectile motion:
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