Final answer:
To find the range of the marble when fired horizontally, we can use the fact that the horizontal motion is independent of the vertical motion. We use the equation y = 1/2gt^2 to find the time it takes for the marble to hit the ground. Then, we can find the horizontal displacement using the equation x = v*t.
Step-by-step explanation:
In order to find the range of the marble when fired horizontally, we can use the fact that the horizontal motion is independent of the vertical motion. When the marble is fired horizontally, its initial vertical velocity is 0 m/s and it falls freely under gravity. Using the equation y = 1/2gt^2, where y is the vertical displacement and g is the acceleration due to gravity, we can find the time it takes for the marble to hit the ground. Since the marble is fired from a height of 1.5 m, the vertical displacement is -1.5 m. Solving for t, we get t = sqrt(2y/g), where g = 9.8 m/s^2. Plugging in the values, we find t = sqrt(2*(-1.5)/9.8) = 0.55 s.
Now, we can find the horizontal displacement using the equation x = v*t, where x is the horizontal displacement, v is the horizontal velocity, and t is the time. Since the marble is fired horizontally, its initial horizontal velocity is the same as the initial velocity of the spring-loaded gun, which we will denote as v0. So, x = v0*t. We are not given the value of v0 in the question, so we cannot determine the exact range of the marble. However, we know that the time it takes for the marble to hit the ground is 0.55 s, so the horizontal displacement will be x = v0 * 0.55.
To draw a diagram of the situation, we can represent the vertical motion of the marble as a parabolic trajectory and the horizontal motion as a straight line.