A ball is thrown horizontally at 15 m/s from a clifftop 70 m above the sea level. Find:
a) the time to land;
b) the angle at which it hits the water;
° below the horizontal
c) the speed at which it hits the water.
m/s
how long does it take a ball to fall 70m?
what horizontal distance does it travel in that time?
doesnt say, but i already solved for time,3.78s
35
To solve this problem, we can use the principles of projectile motion. Let's break down each part of the question separately and explain how to find the answers.
a) The time to land:
Since the ball is thrown horizontally, there is no vertical initial velocity. The only force acting on the ball in the vertical direction is acceleration due to gravity (g = 9.8 m/s^2). We need to find the time it takes for the ball to fall from a height of 70 m to the ground.
The equation to calculate the time of flight (t) for vertical motion is:
h = (1/2)gt^2
Where:
h is the height (70 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time of flight.
Rearranging the equation, we can solve for t:
t^2 = (2h)/g
t = √((2h)/g)
Plugging in the values:
t = √((2 * 70)/9.8)
t ≈ 3.18 seconds
Therefore, it will take approximately 3.18 seconds for the ball to land.
b) The angle at which it hits the water (° below the horizontal):
Since the ball is thrown horizontally, it does not have an initial vertical velocity. Thus, the angle at which it hits the water will be 90° (straight down) since gravity only acts vertically.
c) The speed at which it hits the water:
The speed of the ball can be calculated using the equation:
v = u + at
Where:
v is the final velocity, u is the initial velocity, a is acceleration, and t is time.
Since the ball is thrown horizontally, the initial vertical velocity is 0. Therefore, the initial velocity (u) is the same as the horizontal velocity, which is 15 m/s.
For vertical motion, the acceleration (a) is the acceleration due to gravity, which is -9.8 m/s^2 (negative because it acts downward).
Plugging in the values:
v = 15 + (-9.8) * 3.18
v ≈ -12.03 m/s (negative sign indicates downward direction)
Therefore, the ball hits the water with a speed of approximately 12.03 m/s.