Question

Forensic Investigation - Projectile Motion Background: Mrs. St. Pierre called the police to report a case of vandalism. She claims that while she was at work, the Johnson boys next door deliberately launched a baseball through her living room window with their automatic pitching machine. An officer took their statement. "It was an accident, officer," said 12-year-old Andrew. "I was setting up the machine for my brother Thor to bat. When I tried to walk away, my shoestring got caught on this bolt. I tripped and knocked the machine sideways just as the ball launched." He went on to state that they knocked on Mrs. St. Pierre's door so that they could explain, but when they discovered she wasn't home, they just waited to hear from her later. Instead, she called the police. She insists the boys are a rambunctious pair headed for trouble. She believes their behavior needs to be stopped and wants to press charges. The police began an investigation. Upon initial examination of the scene, the officers found the following: The neighborhood was flat and level. The pitching machine had been put away in the Johnson's garage. There were no indentations from the feet of the machine or dragging tracks in either yard or driveway. The location of the baseball in Mrs. St. Pierre's living room showed roughly the horizontal angle at which the ball was launched, which corresponded with the boys' story. The hole in the window was measured to be 2.43 m above the ground. According to the account given by the Johnson boys, the ball launcher was approximately 15.24 m from Mrs. St. Pierre's window (at the end of their driveway). Further examination of the machine showed that there is only one setting for the pitch. The angle of launch is 30° and the ball exit is 1.21 m above the ground. The exit velocity of the machine is given as 64 km/h. The investigators (you) must determine whether the boys' story could be plausible or if the machine had to be moved closer to (or further from) her window in order to break it. Task: Determine whether the Johnson boys could be telling the truth, or if they are lying about how Mrs. St. Pierre's window was broken. Show your calculations and explain your answer.

Forensic Investigation - Projectile Motion

Background:

Mrs. St. Pierre called the police to report a case of vandalism. She claims that while she was at work, the Johnson boys next door deliberately launched a baseball through her living room window with their automatic pitching machine. An officer took their statement.

"It was an accident, officer," said 12-year-old Andrew. "I was setting up the machine for my brother Thor to bat. When I tried to walk away, my shoestring got caught on this bolt. I tripped and knocked the machine sideways just as the ball launched."

He went on to state that they knocked on Mrs. St. Pierre's door so that they could explain, but when they discovered she wasn't home, they just waited to hear from her later. Instead, she called the police. She insists the boys are a rambunctious pair headed for trouble. She believes their behavior needs to be stopped and wants to press charges.

The police began an investigation. Upon initial examination of the scene, the officers found the following:

The neighborhood was flat and level. The pitching machine had been put away in the Johnson's garage. There were no indentations from the feet of the machine or dragging tracks in either yard or driveway. The location of the baseball in Mrs. St. Pierre's living room showed roughly the horizontal angle at which the ball was launched, which corresponded with the boys' story. The hole in the window was measured to be 2.43 m above the ground.

According to the account given by the Johnson boys, the ball launcher was approximately 15.24 m from Mrs. St. Pierre's window (at the end of their driveway). Further examination of the machine showed that there is only one setting for the pitch. The angle of launch is 30° and the ball exit is 1.21 m above the ground. The exit velocity of the machine is given as 64 km/h. The investigators (you) must determine whether the boys' story could be plausible or if the machine had to be moved closer to (or further from) her window in order to break it.

Task:

Determine whether the Johnson boys could be telling the truth, or if they are lying about how Mrs. St. Pierre's window was broken. Show your calculations and explain your answer.

Forensic Investigation - Projectile Motion

Background:

Mrs. St. Pierre called the police to report a case of vandalism. She claims that while she was at work, the Johnson boys next door deliberately launched a baseball through her living room window with their automatic pitching machine. An officer took their statement.

"It was an accident, officer," said 12-year-old Andrew. "I was setting up the machine for my brother Thor to bat. When I tried to walk away, my shoestring got caught on this bolt. I tripped and knocked the machine sideways just as the ball launched."

He went on to state that they knocked on Mrs. St. Pierre's door so that they could explain, but when they discovered she wasn't home, they just waited to hear from her later. Instead, she called the police. She insists the boys are a rambunctious pair headed for trouble. She believes their behavior needs to be stopped and wants to press charges.

The police began an investigation. Upon initial examination of the scene, the officers found the following:

The neighborhood was flat and level. The pitching machine had been put away in the Johnson's garage. There were no indentations from the feet of the machine or dragging tracks in either yard or driveway. The location of the baseball in Mrs. St. Pierre's living room showed roughly the horizontal angle at which the ball was launched, which corresponded with the boys' story. The hole in the window was measured to be 2.43 m above the ground.

According to the account given by the Johnson boys, the ball launcher was approximately 15.24 m from Mrs. St. Pierre's window (at the end of their driveway). Further examination of the machine showed that there is only one setting for the pitch. The angle of launch is 30° and the ball exit is 1.21 m above the ground. The exit velocity of the machine is given as 64 km/h. The investigators (you) must determine whether the boys' story could be plausible or if the machine had to be moved closer to (or further from) her window in order to break it.

Task:

Determine whether the Johnson boys could be telling the truth, or if they are lying about how Mrs. St. Pierre's window was broken. Show your calculations and explain your answer.

Added by Corey S.

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