Answer:
Less than Mercury's
Explanation:
According to third Kepler's law, the square of the planet's orbital period is proportional to the cube of the average orbital radius of the planet's orbit. The constant of proportionality depends only on the mass of the star, recall that 51 Peg has the same mass as the Sun. Since the orbital period of this planet is less than Mercury's, its average orbital radius is less than Mercury's.
Answer:
A friend snorkeling just below the surface of the water along the same shore will detect the sound first.
Explanation:
- The speed of sound in water medium is faster than that through the air.
- Sound propagates through the medium by transferring through the molecules on it. Water has more closely packed molecules due to which the speed is faster.
- In fact, the sound's speed in water is almost four times faster than that in the air.
- So the guy in the water surface gets to hear sound faster than the one in sore.
<span>The ball clears by 11.79 meters
Let's first determine the horizontal and vertical velocities of the ball.
h = cos(50.0)*23.4 m/s = 0.642788 * 23.4 m/s = 15.04 m/s
v = sin(50.0)*23.4 m/s = 0.766044 * 23.4 m/s = 17.93 m/s
Now determine how many seconds it will take for the ball to get to the goal.
t = 36.0 m / 15.04 m/s = 2.394 s
The height the ball will be at time T is
h = vT - 1/2 A T^2
where
h = height of ball
v = initial vertical velocity
T = time
A = acceleration due to gravity
So plugging into the formula the known values
h = vT - 1/2 A T^2
h = 17.93 m/s * 2.394 s - 1/2 9.8 m/s^2 (2.394 s)^2
h = 42.92 m - 4.9 m/s^2 * 5.731 s^2
h = 42.92 m - 28.0819 m
h = 14.84 m
Since 14.84 m is well above the crossbar's height of 3.05 m, the ball clears. It clears by 14.84 - 3.05 = 11.79 m</span>
